九州大学 研究者情報
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基本情報 研究活動 教育活動 社会活動
ADE IRMA SURIAJAYA(あで いるま すりあじやや) データ更新日:2021.08.03



主な研究テーマ
ゼータ関数とL関数およびそれらの導関数の零点と値の分布
キーワード:ゼータ関数、L関数、導関数、零点、値分布
2013.06.
研究業績
主要原著論文
1. 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..
2. 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.
3. 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
$0<\Im s\le T$. We further apply our method and obtain a zero counting formula for the derivative of Selberg zeta functions, improving earlier work of Luo~\cite{Luo}..
4. 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.
5. 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.
6. 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.
7. 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.
8. Daniel A. Goldston, Ade Irma Suriajaya, A singular series average and the zeros of the Riemann zeta-function, to appear in Acta Arith., 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..
主要総説, 論評, 解説, 書評, 報告書等
主要学会発表等
1. 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..
2. 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].
3. 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.
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)
2018年度~2020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.

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