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

#### 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 isamong a collection of subsets of Z/qZ that we describe. These formulasextend two formulas of D. Shanks in the sixties and lead to very fastnumerical evaluation in some cases. We shall show the link between ourformulas and abelian field theory. We will continue our journey withsome problems on the existence of primes in the coset of some subgroupof (Z/qZ)^x of finite index. This is based on joined works with R.Balasubramanian, S. Ettahri, S. Laishram, P. Srivastav and L. Surel.Google meet link for this talk ismeet.google.com/rzt-jmep-hmt

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