Associate Professor Tatsushi Tanaka

Area and Subject Taught Algebra
Research Theme(s) Multiple Zeta Values, Number Theory
Academic Degrees Doctor (Mathematics), Kyushu University
Keywords for Research Field Number Theory, Multiple Zeta Values, Multiple L-Values
Office Phone Number Not Public
e-mail Not Public

Research Overview

I’m working on number theory, particularly (Euler-Zagier) multiple zeta values (MZVs for short). MZVs are real numbers defined as generalization of Riemann zeta values. This research subject has connection with various theories such as Bernoulli numbers, free Lie algebras, modular forms, special functions, knot theory, mixed Tate motives, the Grothendieck-Teichmüller group, quantum field theory, conformal field theory, etc. Several variations of MZVs, e.g., multiple Hurwitz zeta values, multiple L-values, p-adic MZVs, and q-analogue of MZVs, have been studied. At present I’m interested mainly in the structure of MZV algebra. Computer algebra systems, PARI/GP and Risa/Asir, are of great use in my research. So far I’ve succeeded for instance in verifying the quasi-derivation relation for MZVs (which was a conjecture by M. Kaneko and D. Zagier), introducing linear operators to stratify the cyclic sum formula (CSF) and then showing the CSF is included in a class of relations proved by Kawashima, and proving that certain sum of non-strict MZVs is a power of π with rational multiplication.

Notable Publications and Works in the Last Three Years

  1. Rooted tree maps and Kawashima relations for multiple zeta values (with H. Bachmann), preprint (arXiv: 1801.05381).
  2. Rooted tree maps and the derivation relation for multiple zeta values (with H. Bachmann), to appear in IJNT.
  3. Rooted tree maps, preprint (arXiv: 1712.01029).
  4. Kawashima’s relations for interpolated multiple zeta values (with N. Wakabayashi), J. Algebra 447, 424-431 (2016).