Title: From value distribution until approximation: zeta-functions and their classes / Nuo reikšmių pasiskirstymo iki aproksimavimo: dzeta funkcijos ir jų klasės
Acronym: VaDisZeta
Grant No.: S-LJP-25-1
Duration: 2025-07-01 – 2027-06-30
Annotation:
The Riemann zeta-function ζ(s) is the most important function in number theory. It is well-known that all non-trivial zeros of ζ(s) lie in the critical strip 0≤Re(s)≤1. Nevertheless, the Riemann hypothesis remains open. It states that all non-trivial zeros of ζ(s) are distributed on the line Re(s)=1/2. We mention the close relation between non-trivial zeros and the distribution of prime numbers. This is one of the reasons why it is so valuable to study the behaviour of ζ(s), its logarithms and derivatives inside the critical strip. It is nonetheless significant to obtain analogous results for other zeta- and L-functions and some classes. This could potentially allow us to solve a list of actual and significant problems: finding large values, extending applications of the resonance method, developing M-functions theory, estimating mean value, distribution of zeros, approximation by zeta-functions‘ shifts, effectivization.
Project aims to conduct research on joint value-distribution and approximation for various generalizations of the Riemann zeta-function by other zeta- and L-functions and collections of classes, with emphasis on the Pankowski class, which has not yet been studied in depth. The main attention will be focused on the joint value-distribution of two classes, namely, Matsumoto and Pankowski.
Team leaders:
- in Lithuania, Dr Roma Kačinskaitė (Associate Professor, Vilnius University)
- in Japan, Dr Kohji Matsumoto (Professor, Aichi Institute of Technology, and Professor Emeritus, Nagoya University)
Team members:
- Dr Kenta Endo (Assistant Professor, National Institute of Technology, Suzuka College)
- Dr Shota Inoue (Assistant Professor, Nihon University)
- Dr Masahiro Mine (Lecturer, Waseda University)
- Dr Hidehiko Mishou (Professor, Tokyo Denki University)
- Dr Hirofumi Nagoshi (Associate Professor, Gunma University)
- Keita Nakai (Graduate Student, Nagoya University)
- Benjaminas Togobickij (Doctoral Student, Vilnius University)
Funding:
The project is supported under the bilateral programme of the Research Council of Lithuania (LMT) and the Japan Society for the Promotion of Science (JSPS) (see https://lmt.lrv.lt/en/research-funding/international-collaborations/lithuania-japan/).