Suriajaya Ade Irma | Last modified date：2024.06.03 |

Associate Professor /
Division of Algebra and Geometry /
Faculty of Mathematics

**Presentations**

1. | Shingo Sugiyama, Weighted density conjecture for families of L-functions, Zeta Functions in OKINAWA 2023, 2023.10. |

2. | Shingo Sugiyama, Weighted distribution of low-lying zeros of L-functions in a family, The eleventh Pan Asian Number Theory Conference (PANT 2023-Harbin), 2023.08. |

3. | Ade Irma Suriajaya, A new phenomenon in the weighted one-level density for Dirichlet L-functions, 2024.03. |

4. | Ade Irma Suriajaya, A weighted one-level density for Dirichlet L-functions with a new type of density, MPIM Number Theory Seminar, 2024.03. |

5. | Ade Irma Suriajaya, An Unconditional Montgomery Theorem and Simple Zeros of the Riemann Zeta-Function, Rencontres de théorie analytique et élémentaire des nombres, 2023.09, Assuming the Riemann Hypothesis (RH), Montgomery (1973) proved a theorem concerning the pair correlation of nontrivial zeros of the Riemann zeta-function. One consequence of this theorem was that, under RH, at least 2/3 of the zeros are simple. We show that this theorem of Montgomery holds unconditionally. As an application, under a much weaker hypothesis than RH, we show that at least 61.7% of zeros of the Riemann zeta-function are simple. This weaker hypothesis does not require that any of the zeros are on the half-line. We can further weaken the hypothesis using a density hypothesis. Montgomery's theorem is a statement about the behavior of a certain function within the interval [-1,1] and it is conjectured to hold beyond that interval as well. This conjecture, assuming RH, implies that almost all zeros of the Riemann zeta-function are simple. As opposed to Montgomery's conjecture, the "Alternative Hypothesis" conjectures a completely different behavior of the function. If time allows, I would like to also briefly introduce related results under this Alternative Hypothesis.. |

6. | Ade Irma Suriajaya, An Unconditional Montgomery Theorem and Simple Zeros of the Riemann Zeta-Function, MPIM Number Theory Lunch Seminar, 2023.08. |

7. | Ade Irma Suriajaya, The average number of Goldbach representations and zero-free regions of the Riemann zeta-function, RIMS Workshop 2023: Analytic Number Theory and Related Topics, 2023.10, [URL]. |

8. | Ade Irma Suriajaya, The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta Function, International Conference on Probability Theory and Number Theory 2023, 2023.09. |

9. | Ade Irma Suriajaya, The Pair Correlation Conjecture, the Alternative Hypothesis, and an Unconditional Montgomery Theorem, CIRM Workshop: Universality, Zeta-Functions, and Chaotic Operators, 2023.08, Assuming the Riemann Hypothesis (RH), Montgomery (1973) proved a theorem concerning the pair correlation of nontrivial zeros of the Riemann zeta-function. One consequence of this theorem was that, under RH, at least 2/3 of the zeros are simple. We show that this theorem of Montgomery holds unconditionally. Furthermore, under a much weaker hypothesis than RH, we show that at least 61.7% of zeros of the Riemann zeta-function are simple. This weaker hypothesis does not require that any of the zeros are on the half-line. In this talk, we will also discuss how to improve this result. Montgomery's theorem states an asymptotic behavior of a function F(α) which captures the pair correlation of nontrivial zeros of the Riemann zeta-function in the interval [-1,1] and he gave the now famous "pair correlation conjecture" predicting the behavior of F(α) beyond this integral. This conjecture, also assuming RH, implies that almost all zeros of the Riemann zeta-function are simple. An alternative to Montgomery's conjecture, known as the Alternative Hypothesis (AH) is an antithetical statement that consecutive zeros of the Riemann zeta-function are spaced at multiples of half of their average spacing. This hypothesis arose in the mid 1990s and has been studied by several authors, including Conrey and Iwaniec (2002), Farmer, Gonek and Lee (2014), Baluyot (2016), Lagarias and Rodgers (2020). We examine further consequences of AH and show that, under RH, AH seems to allow for a certain percentage of multiple zeros. We also prove that a slightly stronger version of AH implies that almost all zeros of the Riemann zeta-function are simple. This is joint work with Siegfred Alan C. Baluyot, Daniel Alan Goldston, and Caroline L. Turnage-Butterbaugh.. |

10. | Ade Irma Suriajaya, The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta Function, AMM-ICNA 2023, 2023.05. |

11. | Shingo Sugiyama, Recent progress on the weighted density of low-lying zeros of L-functions in a family, Number Theory in Tokyo, 2023.03. |

12. | Ade Irma Suriajaya, The Pair Correlation Conjecture, the Alternative Hypothesis, and an Unconditional Montgomery Theorem, RIMS Workshop for Women in Zeta Functions and Their Representations, 2023.03, [URL]. |

13. | Ade Irma Suriajaya, Error of the average of Goldbach representations in relation to the prime number theorem, Oberwolfach Workshop 2245: Analytic Number Theory Tuesday Evening Circle of informal talks, 2022.11, ゴールドバッハ表現の個数の平均評価と素数定理の近似公式との関係を明らかにしたことを紹介する。. |

14. | Ade Irma Suriajaya, Zeros of derivatives of L-functions in the Selberg class on the left-half plane and the left-half of the critical strip, RIMS Workshop 2022: Analytic Number Theory and Related Topics, 2022.10, [URL]. |

15. | Ade Irma Suriajaya, Goldbach's Conjecture, the Riemann Hypothesis and problems on twin primes in Number Theory, and recent results relating Goldbach and prime pair problems to zeros of L-functions, Women in Mathematics, 2022.09, Number Theory has a very long history that dates back thousands of years. The main goal of this study is to understand properties of numbers which essentially can be reduced to understanding prime numbers. Although we have the outstanding Prime Number Theorem, more precise information about the distribution of prime numbers is mostly unknown. For example, it is also not known if there are infinitely many pairs of prime numbers having difference 2, the so-called twin prime pairs. Recent breakthroughs in Analytic Number Theory have succeeded in showing the infinitude of prime pairs with small gaps, which is the contribution of Yitang Zhang, one of this year's Fields medalists, James Maynard, and also Terrence Tao. The 280-year-old Goldbach's conjecture and the Riemann hypothesis which is now over 160 years old are also among the most famous yet important unsolved problems in Analytic Number Theory. The Riemann Hypothesis is a conjecture about the location of zeros of the Riemann zeta function. The importance of this problem not only in Number Theory but also many other areas of Mathematics and even Physics is reflected in many known equivalent statements. In Analytic Number Theory alone, we know the equivalence between the Riemann Hypothesis and many prime distribution related problems. Its equivalence to Goldbach related problems is also known. It is important to note that Goldbach's conjecture itself is an independent problem to the Riemann Hypothesis and neither is stronger than the other. In this talk, I would like to introduce a few interesting recent results in this direction.. |

16. | Daniel A. Goldston, Pair Correlation of Zeta-Zeros and Two Problems on Primes, Number Theory Conference in honour of Kálmán Győry – János Pintz – András Sárközy, 2022.07. |

17. | Shingo Sugiyama, The one-level density for Dirichlet L-functions weighted by L-values, 9th Kyoto conference on automorphic forms, 2022.06. |

18. | Ade Irma Suriajaya, Weighted One-level Density of Low-lying Zeros of Dirichlet L-Functions, Arithmetik an der A7, 2022.06. |

19. | Shingo Sugiyama, 対称べき L 関数の低い位置にある零点の重みつき密度について, RIMS共同研究(公開型)「保型形式、保型L関数とその周辺」, 2022.01, [URL]. |

20. | Ade Irma Suriajaya, Goldbach's Conjecture and the Riemann Hypothesis in Number Theory, and Their Relations to Zeta Functions, Catch-all Mathematical Colloquium of Japan, 2022.01. |

21. | Ade Irma Suriajaya, The average number of Goldbach representations, pair correlation of zeros of the Riemann zeta function and error term of the prime number theorem, RIMS Workshop 2021: Analytic Number Theory and Related Topics, 2021.10. |

22. | Ade Irma Suriajaya, The Hardy-Littlewood Goldbach Conjecture and Landau-Siegel zeros, Incheon National University 13th International Symposium on Natural Sciences, 2021.10. |

23. | Ade Irma Suriajaya, The number of Goldbach representations and pair correlation of zeros of the Riemann zeta function, DMV-ÖMG Annual Conference 2021 Algebra, Algebraic Geometry and Number Theory Section, 2021.09. |

24. | Ade Irma Suriajaya, Die Goldbachschen Darstellungen und Landau-Siegel-Nullstellen der Dirichletschen L-Funktionen (Goldbach representations and Landau-Siegel zeros), Arithmetik an der A7, 2021.09. |

25. | Ade Irma Suriajaya, Goldbach representations and exceptional zeros of Dirichlet L-functions, Japan Europe Number Theory Exchange Seminar, 2021.06. |

26. | Daniel Goldston, Goldbach Conjecture and Landau-Siegel Zeros, AIM FRG seminar, 2021.05. |

27. | Ade Irma Suriajaya, Distribution of values of L-functions arising from a Riemann-type functional equation, International Conference on Analytic Number Theory dedicated to 75th anniversary of G.I. Arkhipov and S.M. Voronin, 2020.12. |

28. | Ade Irma Suriajaya, Error term of the Riesz mean of Hardy-Littlewood singular series, RIMS Workshop: Problems and Prospects in Analytic Number Theory, 2020.11, [URL]. |

29. | Ade Irma Suriajaya, Zeros of derivatives of the Riemann zeta function and relations to the Riemann hypothesis, Tel Aviv Number Theory seminar, 2020.10. |

30. | Ade Irma Suriajaya, Omega estimate of the error term in the Cesàro mean of the prime pair singular series, 九州大学多重ゼータセミナー, 2020.07. |

31. | Ade Irma Suriajaya, The Julia line of a Riemann-type functional equation, Number Theory during Lockdown, 2020.06. |

32. | Ade Irma Suriajaya, An Upper Bound for Stieltjes Constants of L-functions in the Extended Selberg Class, FCK COVID-19, 2020.04. |

33. | Ade Irma Suriajaya, Value distribution of the Riemann zeta function around its Julia lines, The 13th Young Mathematicians Conference on Zeta Functions, 2020.02, [URL]. |

34. | Ade Irma Suriajaya, Improved error estimate for the number of zeros of the derivatives of the Riemann zeta function, RIMS Workshop: Analytic Number Theory and Related Topics, 2019.10. |

35. | Ade Irma Suriajaya, Schemmel's function and its associated mean-values, 2019.09. |

36. | Ade Irma Suriajaya, On the error term estimate for the number of zeros of the derivatives of the Riemann zeta function, Oberseminar Zahlentheorie, 2019.08. |

37. | Ade Irma Suriajaya, Distribution of zeros of the derivatives of the Riemann zeta function and its relations to zeros of the zeta function itself, Boston University/Keio University Workshop 2019, 2019.06, Speiser in 1935 showed that the Riemann hypothesis, which claims that all nontrivial zeros of the Riemann zeta function lie on the straight line Re(s)=1/2, is equivalent to the first derivative of the Riemann zeta function having no zeros in the left-half of the critical strip. This result shows that the distribution of zeros of the Riemann zeta function is related to that of its derivatives. The number of zeros and the distribution of the real part of non-real zeros of the derivatives of the Riemann zeta function have been investigated by Berndt, Levinson, Montgomery, Akatsuka, Ge and myself. Berndt, Levinson, and Montgomery investigated the general case, meanwhile Akatsuka gave sharper estimates, which was further improved by Ge, for the first derivative case, under the truth of the Riemann hypothesis. I extended Akatsuka's result to higher order derivatives before the existence of Ge's result. Ge and I were later able to extend his idea to the case of higher order derivatives. I would like to introduce some important results in this direction, especially on how they are related to the distribution of zeros of the Riemann zeta function itself. Finally, I hope to be able to introduce necessary details for the improvement Ge and I obtained.. |

38. | Ade Irma Suriajaya, Generalized Schemmel's function and its associated mean-values, The fifth mini symposium of the Roman Number Theory Association, 2019.04. |

39. | Ade Irma Suriajaya, Mean-values associated with Schemmel's function, Oberseminar Zahlentheorie, 2019.04. |

40. | Ade Irma Suriajaya, New results on the distribution of zeros of the derivatives of the Riemann zeta function, Value distribution of zeta and L-functions and related topics, 2019.03, [URL]. |

41. | Ade Irma Suriajaya, The multiplication theorem of the Hurwitz zeta function by using sum of gaps in two-generated numerical semigroups, 2019.02. |

42. | Ade Irma Suriajaya, An upper bound for Stieltjes constants of L-functions in the Selberg class, Number Theory Mini Workshop at Sophia, 2019.01. |

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44. | Ade Irma Suriajaya, Zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, Number Theory Down Under 6, 2018.09. |

45. | Ade Irma Suriajaya, Values of the Riemann zeta function on vertical arithmetic progressions in the critical strip, International Conference on Number Theory Dedicated to the 70th Birthdays of Professors Antanas Laurinčikas and Eugenijus Manstavičius, 2018.09. |

46. | Ade Irma Suriajaya, Values of the Riemann zeta function on vertical arithmetic progressions in the critical strip, Conference on elementary and analytic number theory (ELAZ) 2018, 2018.09. |

47. | Ade Irma Suriajaya, Values of the Riemann zeta function on vertical arithmetic progressions in the critical strip, The 15th Canadian Number Theory Association Conference, 2018.07. |

48. | Ade Irma Suriajaya, Values of the Riemann zeta function on vertical arithmetic progressions in the critical strip, Oberseminar Zahlentheorie, 2018.05. |

49. | Ade Irma Suriajaya, Zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, Oberseminar Modularfunktionen, 2018.05. |

50. | Ade Irma Suriajaya, Zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, 2018.05. |

51. | Ade Irma Suriajaya, An approximate functional equation for the fourth moment of the Riemann zeta function on the critical line, Oberseminar Zahlentheorie, 2018.04. |

52. | Ade Irma Suriajaya, Zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, The fourth mini symposium of the Roman Number Theory Association, 2018.04, Speiser in 1935 showed that the Riemann hypothesis is equivalent to the first derivative of the Riemann zeta function having no zeros on the left-half of the critical strip. This result shows that the distribution of zeros of the Riemann zeta function is related to that of its derivatives. The number of zeros and the distribution of the real part of non-real zeros of the derivatives of the Riemann zeta function have been investigated by Berndt, Levinson, Montgomery, and Akatsuka. Berndt, Levinson, and Montgomery investigated the general case, meanwhile Akatsuka gave sharper estimates under the truth of the Riemann hypothesis. This result is further improved by Ge. In the first half of this talk, we introduce these results and generalize the result of Akatsuka to higher-order derivatives of the Riemann zeta function.Analogous to the case of the Riemann zeta function, the number of zeros and many other properties of zeros of the derivatives of Dirichlet L-functions associated with primitive Dirichlet characters were studied by Yildirim. In the second-half of this talk, we improve some results shown by Yildirim for the first derivative and show some new results. We also introduce two improved estimates on the distribution of zeros obtained under the truth of the generalized Riemann hypothesis. We also extend the result of Ge to these Dirichlet L-functions when the associated modulo is not small. Finally, we introduce an equivalence condition analogous to that of Speiser’s for the generalized Riemann hypothesis, stated in terms of the distribution of zeros of the first derivative of Dirichlet L-functions associated with primitive Dirichlet characters.. |

53. | Ade Irma Suriajaya, Values of the Riemann zeta function on vertical arithmetic progressions in the critical strip, Analytic Number Theory Seminar, 2018.02. |

54. | Ade Irma Suriajaya, Some improvements in estimates related to the distribution of zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, RIMS Workshop: Analytic Number Theory and Related Areas, 2017.10. |

55. | Ade Irma Suriajaya, Distribution of zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, Symposium for South Asian Women in Mathematics, 2017.10. |

56. | Ade Irma Suriajaya, An approximate functional equation for the fourth moment of the Riemann zeta function on vertical arithmetic progressions on the critical line, Oberseminar Zahlentheorie, 2017.10. |

57. | Ade Irma Suriajaya, Distribution of zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, 2017.09. |

58. | Ade Irma Suriajaya, Values of the Riemann zeta function on vertical arithmetic progressions in the critical strip, Number Theory Week 2017 -- A conference on the occasion of the 60th birthday of Jerzy Kaczorowski, 2017.09. |

59. | Ade Irma Suriajaya, Values of the Riemann zeta function on vertical arithmetic progressions in the critical strip, Various Aspects of Multiple Zeta Functions –– Conference in Honor of Kohji Matsumoto’s 60th Birthday, 2017.08, [URL]. |

60. | Ade Irma Suriajaya, Zeros of the Riemann zeta function and its derivatives, KMITL Number theory seminar, 2017.07. |

61. | Ade Irma Suriajaya, Distribution of zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, International Conference in Number Theory and Applications -- Conference in Honor of Vichain Laohakosol, 2017.07. |

62. | Ade Irma Suriajaya, A new zero-free region for the first derivative of Dirichlet L-functions, Oberseminar Zahlentheorie, 2017.07. |

63. | Ade Irma Suriajaya, An ergodic value distribution of certain meromorphic functions, 30th Journées Arithmétiques, 2017.07. |

64. | Ade Irma Suriajaya, On the distribution of zeros of the first derivative of Dirichlet L-functions, Connections for Women: Analytic Number Theory, 2017.02. |

65. | Ade Irma Suriajaya, Distribution of zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, Number Theory Seminar, 2016.12. |

66. | Ade Irma Suriajaya, Distribution of zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, Algebra and Number Theory Seminar, 2016.11. |

67. | Ade Irma Suriajaya, On the distribution of zeros of the first derivative of Dirichlet L-functions, The Sixth International Conference Analytic and Probabilistic Methods in Number Theory, 2016.09. |

68. | Ade Irma Suriajaya, On the distribution of zeros of the first derivative of Dirichlet L-functions, Conference on elementary and analytic number theory (ELAZ) 2016, 2016.09. |

69. | Ade Irma Suriajaya, On the distribution of zeros of the first derivative of Dirichlet L-functions, Conference on elementary and analytic number theory (ELAZ) 2016, 2016.09. |

70. | Ade Irma Suriajaya, Ergodic value distribution of zeta functions and L-functions, Number Theory Day, 2016.08. |

71. | Ade Irma Suriajaya, Distribution of zeros of the first derivative of Dirichlet L-functions, Number Theory Seminar, 2016.06. |

72. | Ade Irma Suriajaya, Distribution of zeros of the first derivative of Dirichlet L-functions, 2016.06. |

73. | Ade Irma Suriajaya, An analogue of Speiser's theorem for Dirichlet L-functions, Analytic Number Theory Seminar, 2016.06. |

74. | Ade Irma Suriajaya, On the distribution of zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, Zeta Functions of Several Variables and Applications, 2015.11. |

75. | Ade Irma Suriajaya, An ergodic value distribution of some class of zeta and L-functions, Analytic Number Theory Seminar, 2015.10. |

76. | Ade Irma Suriajaya, On the distribution of zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, Arithmetic 2015: Silvermania, 2015.08. |

77. | Ade Irma Suriajaya, Some results on the zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, 29th Journées Arithmétiques, 2015.07. |

78. | Ade Irma Suriajaya, On the distribution of zeros of the derivatives of the Riemann zeta function and Dirichlet L-functions, Arithmetik an der A7, 2015.07. |

79. | Ade Irma Suriajaya, On the Zeros of the Derivatives of the Riemann Zeta Function and Dirichlet L-functions, Seminar / Colloquium on Mathematics Research (Nagoya University - Gadjah Mada University), 2015.03. |

80. | Ade Irma Suriajaya, Two Estimates on the Zeros of L'(s,χ) under the Generalized Riemann Hypothesis, Analytic Number Theory Seminar, 2014.12. |

81. | Ade Irma Suriajaya, On the zeros of the derivatives of the Riemann zeta function under the Riemann hypothesis, RIMS Workshop: Analytic Number Theory – Distribution and Approximation of Arithmetic Objects, 2014.10. |

82. | Ade Irma Suriajaya, On the Zeros of the k-th Derivative of the Riemann Zeta Function under the Riemann Hypothesis, International Congress of Mathematicians 2014, 2014.08. |

83. | Ade Irma Suriajaya, On the Zeros of the Derivatives of the Riemann Zeta Function under the Riemann Hypothesis, International Congress of Women Mathematicians, 2014.08. |

84. | Ade Irma Suriajaya, On the Zeros of the k-th Derivative of the Riemann Zeta Function under the Riemann Hypothesis, Analytic Number Theory Workshop, 2014.05. |

85. | Ade Irma Suriajaya, On the Zeros of the k-th Derivative of the Riemann Zeta Function under the Riemann Hypothesis, 第7回ゼータ若手研究集会, 2014.02. |

86. | Ade Irma Suriajaya, On the Zeros of the Second Derivative of the Riemann Zeta Function under the Riemann Hypothesis, The 7th Japan-China Seminar on Number Theory, 2013.10. |

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