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Ade Irma Suriajaya Last modified date:2024.05.05





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Homepage
https://kyushu-u.elsevierpure.com/en/persons/suriajaya-ade-irma
 Reseacher Profiling Tool Kyushu University Pure
Academic Degree
Doctor of Philosophy (Mathematical Science), Master of Mathematical Science
Country of degree conferring institution (Overseas)
Yes Bachelor
Field of Specialization
Algebra (Analytic Number Theory)
ORCID(Open Researcher and Contributor ID)
0000-0003-3386-0990
Total Priod of education and research career in the foreign country
01years10months
Outline Activities
Keywords: zeta functions, L-functions, derivatives, zeros, value distribution, prime numbers, Goldbach problems
Kakenhi project number: 18K13400, 22K13895
Member of Mathematical Society of Japan
(From May 2019 on:) Visiting scientist of RIKEN iTHEMS
Research
Research Interests
  • Distribution of zeros and values of zeta functions and L-functions and their derivatives, connection to the distribution of prime numbers
    keyword : zeta functions, L-functions, derivatives, zeros, value distribution, distribution of prime numbers
    2013.06.
Current and Past Project
  • The Riemann Zeta Function and Distribution of Prime Gaps
  • Zeros of zeta functions and L-functions, and their relations to Goldbach's problem
  • Zeros and discrete value distribution of the Riemann zeta function and its derivatives
Academic Activities
Papers
1. Keith Billington, Maddie Cheng, Jordan Schettler, Ade Irma Suriajaya, The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function, In this paper, we prove an unconditional form of Fujii's formula for the average number of Goldbach representations and show that the error in this formula is determined by a general zero-free region of the Riemann zeta-function, and vice versa. In particular, we describe the error in the unconditional formula in terms of the remainder in the Prime Number Theorem which connects the error to zero-free regions of the Riemann zeta-function..
2. Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya, Caroline L. Turnage-Butterbaugh, An Unconditional Montgomery Theorem for Pair Correlation of Zeros of the Riemann Zeta Function, Acta Arith., 10.4064/aa230612-20-3, Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem concerning pair correlation of zeros of the Riemann zeta-function. One consequence of this theorem is that, assuming RH, at least 67.9% of the nontrivial zeros are simple. Here we obtain an unconditional form of Montgomery's theorem and show how to apply it to prove the following result on simple zeros: Assuming all the zeros ρ=β+iγ of the Riemann zeta-function such that T^{3/8}
3. Daniel A. Goldston, Ade Irma Suriajaya, On an Average Goldbach Representation Formula of Fujii, Nagoya Math. J., 10.1017/nmj.2022.44, 250, 511-532, 2023.01.
4. John B. Friedlander, Daniel A. Goldston, Henryk Iwaniec, Ade Irma Suriajaya, Exceptional zeros and the Goldbach problem, J. Number Theory, 10.1016/j.jnt.2021.06.004, 233, 78-86, 2022.04, We show that the assumption of a weak form of the Hardy-Littlewood conjecture on the Goldbach problem suffices to disprove the possible existence of exceptional zeros of Dirichlet L-functions..
5. Daniel A. Goldston, Ade Irma Suriajaya, The error term in the Cesàro mean of the prime pair singular series, J. Number Theory, 10.1016/j.jnt.2021.03.004, 227, 144-157, 2021.10, We show that the error term in the asymptotic formula for the Ces{\`a}ro mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures cannot be too small and oscillates..
6. Daniel A. Goldston, Ade Irma Suriajaya, A singular series average and the zeros of the Riemann zeta-function, Acta Arith., 10.4064/aa200821-24-2, 200, 71-90, 2021.06, We show that the Riesz mean of the singular series in the Goldbach and the Hardy-Littlewood Prime Pair Conjectures has an asymptotic formula with an error term that can be expressed as an explicit formula that depends on the zeros of the Riemann zeta-function. Unconditionally this error term can be shown to oscillate, while conditionally it can be shown to oscillate between sharp bounds..
7. Junghun Lee, Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya, The Values of the Riemann Zeta-Function on Discrete Sets, Advanced Studies in Pure Mathematics, Proceedings of Various Aspects of Multiple Zeta Functions — in honor of Professor Kohji Matsumoto’s 60th birthday, 10.2969/aspm/08410315, 84, 315-334, 2020.04.
8. Fan Ge, Ade Irma Suriajaya, Note on the number of zeros of $\zeta^{(k)}(s)$, Ramanujan J., 10.1007/s11139-019-00219-z, 55, 661-672, 2020.03, Assuming the Riemann hypothesis, we prove that
$$
N_k(T) = \frac{T}{2\pi}\log \frac{T}{4\pi e} + O_k\left(\frac{\log{T}}{\log\log{T}}\right),
$$
where $N_k(T)$ is the number of zeros of $\zeta^{(k)}(s)$ in the region
$0
9. Hirotaka Akatsuka, Ade Irma Suriajaya, Zeros of the first derivative of Dirichlet L-functions, J. Number Theory, 10.1016/j.jnt.2017.08.023, 184, 300-329, 2018.03.
10. Ade Irma Suriajaya, Two estimates on the distribution of zeros of the first derivative of Dirichlet L-functions under the generalized Riemann hypothesis, J. Théor. Nombres Bordeaux, 10.5802/jtnb.988, 29, 2, 471-502, 2017.05.
11. Junghun Lee, Ade Irma Suriajaya, An ergodic value distribution of certain meromorphic functions, J. Math. Anal. Appl., 10.1016/j.jmaa.2016.07.064, 445, 1, 125-138, 2017.01.
12. Ade Irma Suriajaya, On the zeros of the k-th derivative of the Riemann zeta function under the Riemann hypothesis, Funct. Approx. Comment. Math, 10.7169/facm/2015.53.1.5, 53, 1, 69-95, 2015.10.
Presentations
1. 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..
2. 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..
3. 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].
4. 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..
5. 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.
6. 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..
7. Ade Irma Suriajaya, Generalized Schemmel's function and its associated mean-values, The fifth mini symposium of the Roman Number Theory Association, 2019.04.
8. 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..
Awards
  • Nagoya University Outstanding Graduate Student Award
Educational
Educational Activities
I am currently mainly teaching exercise classes for undergraduate math students. From 2014 to 2020, I taught mathematics in English at Meiwa High School once per year.
I taught Multivariable Calculus as a part-time lecturer at Sophia University before entering Kyushu University.
I was actively involved in education as a teaching assistant and research assistant during graduate studies.
I also taught several catch-up classes in undergraduate and was a teaching assistant for Calculus and C Programming.
As a part of Kyushu University SENTAN-Q training program, I also taught at San Jose State University in the spring semester of 2023 (Math 226 - Graduate course in Number Theory), co-teaching with Prof. Jordan Schettler.
Social
Professional and Outreach Activities
I am actively giving talks and lectures to general audience..