On 10 September, an international scientific workshop, “Zeta Functions and Their Classes: Results and Problems in Various Aspects,” began at the Vilnius University Faculty of Mathematics and Informatics (VU MIF). Over three days, mathematicians from Lithuania, Japan, France, Germany, Austria and Poland will discuss current research on various zeta functions, their properties and applications.
Workshop participants gathered at VU MIF and joined remotely
The workshop is organised as part of the bilateral Lithuanian–Japanese research project “From Value Distribution until Approximation: Zeta-Functions and Their Classes.” The project is funded by the Research Council of Lithuania (LMT) and the Japan Society for the Promotion of Science (JSPS), under grants S-LJP-25-1 and JPJSBP 120254202.
At the heart of the workshop is research into zeta functions. One of the best known is the Riemann zeta function, which holds a special place in number theory.
It is closely connected with the distribution of prime numbers and one of the most famous unsolved problems in mathematics – the Riemann Hypothesis. Researchers also study the much broader family of zeta and L-functions, as well as various classes of zeta functions, their zeros, value distribution, universality, extreme values and other important properties.
Prof. Roma Kačinskaitė
“We have world-class stars here,” says Prof. Roma Kačinskaitė, one of the workshop organisers and a professor in the Department of Probability Theory and Number Theory at the VU MIF Institute of Mathematics. “Workshop participants will have an opportunity to learn about the latest achievements of researchers from Lithuania, Japan, and other countries, share their research findings, and discuss current problems in number theory and future directions in the field.”
Prof. Kačinskaitė is organising the workshop together with Prof. Kohji Matsumoto of the Institute of Technology, Aichi, Japan.
Prof. Kohji Matsumoto
Prof. Kohji Matsumoto is an internationally recognised Japanese mathematician whose research focuses primarily on zeta functions and analytic number theory. In 1990, he introduced a zeta function that later became known as the Matsumoto zeta function. He is particularly well known for his contributions to the study of the value distribution, universality and analytic properties of zeta functions.
Why zeta functions
Zeta functions are important to mathematicians because they are connected with one of the fundamental problems of mathematics – prime numbers and their distribution. They are also powerful tools for studying various algebraic and analytical structures and for addressing problems in theoretical physics, statistics and other fields.
Zeta functions have been studied for almost three centuries, with their origins tracing back to the work of the 18th-century Swiss mathematician Leonhard Euler. The name derives from the Greek letter ζ (zeta), which was used in the 19th century by German mathematician Bernhard Riemann to denote one of the most important functions, now known as the Riemann zeta function.
New Insights and Future Research Directions
The workshop program covers a broad range of contemporary research topics. On the first day, a presentation on the discovery of the universality of zeta functions was given by Prof. Habil. Dr Antanas Laurinčikas, one of the world's leading researchers in analytic number theory (VU MIF). Researchers from Japan, France, and Austria also presented their work.
Prof. Kohji Matsumoto and Prof. Antanas Laurinčikas, with Dr Athanasios Sourmelidis behind them
On the second day, participants will hear a presentation by Prof. Kohji Matsumoto, founder of the Japanese school of research on zeta functions, on the distribution of zeros of Euler's double zeta function. There will also be an opportunity to hear Prof. Joern Steuding, a German mathematician and one of the world's leading specialists in zeta functions. Japanese and French mathematicians who were former students of K. Matsumoto and J. Steuding will also give presentations. VU MIF researchers will present their work as well, including Prof. dr. Igoris Belovas from the Intelligent Technologies Research Group at VU MIF DMSTI and Benjaminas Togobickij, a PhD student at the VU MIF Institute of Mathematics.
On the third day, the presentations will once again focus primarily on universality, the distribution of prime numbers and zeta functions. Speakers will include Dr Łukasz Pánkowski (Adam Mickiewicz University, Poland), Dr Hirofumi Nagoshi (Gunma University, Japan), and Prof. Ramūnas Garunkštis (Vilnius University Faculty of Mathematics and Informatics).
“Partnership with Japan provides an opportunity to work with a strong group of researchers in analytic number theory and jointly tackle problems that would be more difficult for a single research group to address,” says Prof. Kačinskaitė. “It is encouraging that this work involves not only researchers with many years of experience, but also young researchers from both countries.”
Prof. Matsumoto and Lithuania
The renowned Japanese mathematician Prof. K. Matsumoto's connection with Lithuania began in 1986, when he met Prof. Jonas Kubilius, one of Lithuania's most prominent 20th-century mathematicians and a pioneer of modern probabilistic number theory, who was then Rector of Vilnius University. Prof. Kačinskaitė first met Prof. Matsumoto at an international conference in Palanga in 2001, although their correspondence and acquaintance, which later developed into joint research and scientific publications, had begun even earlier.
According to Prof. Kačinskaitė, joint publications with Prof. Matsumoto and other international researchers, together with the organization of international events, demonstrate that research by VU MIF mathematicians has become part of the international field of analytic number theory, while the Lithuanian school of mathematics is actively engaged in international research into fundamental mathematical problems.
“The value of this collaboration lies not only in specific proven results. It also strengthens the international visibility of mathematics in Lithuania,” the researcher says.
Presentations and discussions among mathematicians will continue at VU MIF for three days
The international workshop is the result of long-standing collaboration among mathematicians working in this field. The event provides an opportunity not only to present the latest research results, but also to discuss unsolved problems and future directions.
According to Prof. Kačinskaitė, the project is expected to continue by taking the next step – moving from specific zeta functions and the classes currently under investigation towards a broader question: what patterns can be discovered in even wider classes of zeta functions, both in the context of value distribution and universality.
Photos by Vytautas Karpauskas
10 September 2026
