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Ade Irma Suriajaya Last modified date:2020.06.22





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Homepage
https://kyushu-u.pure.elsevier.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
Field of Specialization
Algebra (Analytic Number Theory)
Total Priod of education and research career in the foreign country
00years11months
Outline Activities
Keywords: zeta functions, L-functions, derivatives, zeros, value distribution
Kakenhi project number: 18K13400
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
    keyword : zeta functions, L-functions, derivatives, zeros, value distribution
    2013.06.
Academic Activities
Papers
1. F. Ge, A. I. Suriajaya, Note on the number of zeros of $\zeta^{(k)}(s)$, to appear in Ramanujan J., 10.1007/s11139-019-00219-z, 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}..
2. J. Lee, A. Sourmelidis, J. Steuding, A. I. 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, 84, 315-334, 2020.04.
3. 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.
4. 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.
5. 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.
6. 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, 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..
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.
3. 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..
Awards
  • Nagoya University Outstanding Graduate Student Award
Educational
Educational Activities
I am currently mainly teaching exercise classes for undergraduate math students. Since 2014, I also teach 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.
Social
Professional and Outreach Activities
I am actively giving talks and lectures to general audience..