九州大学-研究者情報 [ADE IRMA SURIAJAYA (准教授) 数理学研究院代数幾何部門]

1.	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.
2.	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..
3.	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..
4.	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..
5.	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.
6.	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
7.	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.
8.	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.
9.	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.
10.	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.

主要総説, 論評, 解説, 書評, 報告書等

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主要学会発表等

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1.	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].
2.	Ade Irma Suriajaya, ゴールドバッハ表現の平均個数評価とリーマンゼータ関数の零点との関係, 筑波セミナー, 2022.11, [URL], 280年前にゴールドバッハは6以上の偶数が必ず二つの奇素数の和として書き表せると予想した。ゴールドバッハ問題を調べるために、偶数を二つの奇素数の和として書き表し、その表し方の個数を数えればよい。それが常に正であることとゴールドバッハ予想が成り立つことと同値である。実際の解析では、正の整数を二つの素数として表現する方法をそのまま数えるより、特殊な関数の重みで数えたほうが数学的に扱いやすい場合がある。そのような重み付き表現は「ゴールドバッハ表現」と通称され、ゴールドバッハ表現の個数の平均評価はリーマンゼータ関数の零点によって与えられる。そのゴールドバッハ表現の個数の平均評価は1991年にFujiiにより初めて与えられたが、リーマン予想が成り立つことを条件としたものである。その評価における誤差項は2010年にBhowmikとSchlage-Puchta、また更に2012年にLanguascoとZaccagniniにより改良された。一般的に、リーマン予想の仮定を外しても、その誤差評価は素数定理の場合とほぼ同様であり、素数を数える場合と同じく、リーマンゼータ関数の非零領域によって記述できる。この講演では、これらの評価を紹介し、また、リーマンゼータ関数の零点に関するいくつかの評価による更なる改良も説明する。この講演で紹介する研究は主にサンノゼ州立大学のDaniel Goldston氏との共同研究である。.
3.	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, [URL], 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..
4.	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.
5.	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, [URL], 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..
6.	Ade Irma Suriajaya, Generalized Schemmel's function and its associated mean-values, The fifth mini symposium of the Roman Number Theory Association, 2019.04, [URL].
7.	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, [URL], 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..

学会活動

所属学会名

日本数学会

学会大会・会議・シンポジウム等における役割

2019.03.21～2019.03.27, Value Distribution of Zeta and L-functions and Related Topics, 実行委員会委員長.

その他の研究活動

海外渡航状況, 海外での教育研究歴

San Jose State University, UnitedStatesofAmerica, 2023.01～2023.05.

American Institute of Mathematics, San Jose State University, UnitedStatesofAmerica, 2023.03～2023.06.

American Institute of Mathematics, San Jose State University, UnitedStatesofAmerica, 2022.08～2022.10.

American Institute of Mathematics, San Jose State University, UnitedStatesofAmerica, 2022.12～2023.02.

Mathematisches Forschungsinstitut Oberwolfach, Germany, 2022.11～2022.11.

University of Würzburg, Germany, 2022.11～2022.11.

University of Würzburg, Germany, 2019.08～2019.08.

University of Würzburg, Germany, 2019.04～2019.04.

China University of Mining and Technology, Beijing, China, 2019.09～2019.09.

Kasetsart University, Thailand, 2019.09～2019.09.

IMSc Chennai, India, 2019.02～2019.02.

University of Würzburg, Germany, 2018.05～2018.06.

University of Würzburg, Germany, 2018.04～2018.04.

UNSW Sydney, Australia, 2018.09～2018.09.

UNSW Canberra, Australia, 2018.09～2018.09.

University of Rochester, UnitedStatesofAmerica, 2018.07～2018.07.

Shandong University Weihai Campus, China, 2018.05～2018.05.

MSRI, UnitedStatesofAmerica, 2018.01～2018.01.

University of Würzburg, Germany, 2017.09～2017.10.

University of Würzburg, Germany, 2017.07～2017.07.

University of Rochester, UnitedStatesofAmerica, 2017.02～2017.03.

University of Rochester, UnitedStatesofAmerica, 2017.05～2017.05.

MSRI, UnitedStatesofAmerica, 2017.05～2017.05.

MSRI, UnitedStatesofAmerica, 2017.01～2017.02.

San Jose State University, UnitedStatesofAmerica, 2017.04～2017.04.

University of Würzburg, Germany, 2016.08～2016.09.

University of Rochester, UnitedStatesofAmerica, 2016.10～2016.12.

Academia Sinica, Taiwan, 2016.06～2016.06.

University of Würzburg, Germany, 2015.06～2015.07.

受賞

名古屋大学学術奨励賞, 名古屋大学, 2015.06.

研究資金

科学研究費補助金の採択状況(文部科学省、日本学術振興会)

2022年度～2026年度, 若手研究, 代表, ゼータ関数及びL関数の零点とゴールドバッハ問題の関係.

2018年度～2022年度, 若手研究, 代表, リーマンゼータ関数およびその導関数の零点と離散的な値の分布.

日本学術振興会への採択状況(科学研究費補助金以外)

2015年度～2016年度, 特別研究員, 代表, リーマンゼータ関数とディリクレのＬ関数の零点.

学内資金・基金等への採択状況

2017年度～2017年度, 理化学研究所　ライフイベントからの復帰支援または、優秀な女性研究者の支援のための資金, ゼータ関数とL関数の導関数の零点.

九大関連コンテンツ

pure2017年10月2日から、「九州大学研究者情報」を補完するデータベースとして、Elsevier社の「Pure」による研究業績の公開を開始しました。

QIR　九州大学学術情報リポジトリシステム情報科学研究院

数理学研究院


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