The Riemann zeta-function ζ(s) is an extremely important function in number theory. It is well known that the distribution of the zeros of ζ(s) is closely connected with the distribution of prime numbers. Therefore the study on the value-distribution of ζ(s) is really significant, but it is surely one of the most difficult branches in analytic number theory, including the celebrated unsolved Riemann Hypothesis. Furthermore, now a lot of generalizations and analogies of ζ(s) are known, and it is equally important to study the value-distribution of those various zeta and L-functions.
Among many known results on the value-distribution of zeta and L-functions, one of the most impressive is the universality property, which roughly implies that any analytic function can be approximated by zeta-functions. It is one of the main aims of the present project to pursue the study of universality theory; this is quite natural, because there are strong schools on universality theory both in Lithuania and in Japan. The project also put into perspective relevant topics such as large values of zeta and L-functions, applications of the resonance method, the theory of M-functions, mean value theorems, effectivization of the universality, and so on.
The following conferences are scheduled to be held.
Conference in Lithuania (September 2026)
Conference in Japan (Spring 2027)
Team Leaders:
- in Japan, Kohji Matsumoto (Aichi Institute of Technology / Nagoya University)
- in Lithuania, Roma Kačinskaitė (Vilnius University)
Team Members:
- Kenta Endo (National Institute of Technology, Suzuka College)
- Shota Inoue (Nihon University)
- Masahiro Mine (Waseda University)
- Hidehiko Mishou (Tokyo Denki University)
- Hirofumi Nagoshi (Gunma University)
- Keita Nakai (Nagoya University)
- Benjaminas Togobickij (Vilnius University)
Funding:
The project is supported by the bilateral program of the Japan Society for the Promotion of Science (JSPS) and the Research Council of Lithuania (LMT).
(Grant Nos. JPJSBP120254202 and S-LJP-25-1)
Reports:
(July 2025) The project began.
(September 2025) Kenta Endo and Keita Nakai visited Lithuania.
- They gave talks at "International Conference on Probability Theory and Number Theory 2025" in Palanga.
- They gave talks at Vilnius University and had a discussion with Roma Kačinskaitė and Benjaminas Togobickij in Vilnius.
(November 2025) Roma Kačinskaitė visited Japan.
- She gave a talk at "Sophia University Mathematics Colloquium" in Tokyo.
- She conducted a joint research with Kohji Matsumoto and Łukasz Pańkowski and had a discussion with Kenta Endo and Keita Nakai in Nagoya.
(November 2025) We held a workshop titled "Analytic Behavior of Zeta Functions -Value Distribution, Universality, and Related Topics-" at Kyushu University in Japan.
- The following project members participated: Kohji Matsumoto, Roma Kačinskaitė, Kenta Endo, Shota Inoue, Masahiro Mine, Hidehiko Mishou, and Keita Nakai.
Acknowledgements:
The project members would like to express their gratitude to the following individuals for organizing relevant meetings.
- Maki Nakasuji (Sophia University)
- Ade Irma Suriajaya (Kyushu University)
- Toshiki Matsusaka (Kyushu University)
Links: