You are cordially invited to the Department of Mathematics Colloquium
Speaker: Syed Waqar Ali Shah (Bilkent University)
“On the Arithmetic of Special Values of the Riemann Zeta Function”
Abstract: The Riemann zeta function occupies a central place in number theory. Its values at positive even integers are rational multiples of powers of $\pi$, while comparatively little is known about its values at positive odd integers. On the other hand, its values at negative integers are described in terms of Bernoulli numbers, which satisfy a rich system of congruences going back to the work of Kummer in the nineteenth century on Fermat’s Last Theorem.
In this talk, I will give a brief overview of classical results on values of the zeta function at integers and explain how the congruences satisfied by its values at negative integers can be reinterpreted from the analytic viewpoint of $p$-adic numbers, where p is a prime. If time permits, I will discuss an algebraic counterpart of this analytic viewpoint stemming from questions on the failure of unique factorization in cyclotomic fields, and how a deep connection between the two developed into the subject now known as Iwasawa theory.
Date: Wednesday, February 11, 2026
Time: 15:40-16:40
Place: Mathematics Seminar Room, SA-141