Wednesday, September 30 2020
19:30 - 20:30

IMSc Webinar

Notes on primes in some special subsets modulo q

Olivier Ramare

Institut de Mathematiques de Luminy

We prove some closed formulas for Euler products of the form
\prod_{p+qZ \in A}R(1/p^s) for a proper rational fraction R, where A is
among a collection of subsets of Z/qZ that we describe. These formulas
extend two formulas of D. Shanks in the sixties and lead to very fast
numerical evaluation in some cases. We shall show the link between our
formulas and abelian field theory. We will continue our journey with
some problems on the existence of primes in the coset of some subgroup
of (Z/qZ)^x of finite index. This is based on joined works with R.
Balasubramanian, S. Ettahri, S. Laishram, P. Srivastav and L. Surel.

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