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On p-adic functions satisfying Kummer type congruences

Posted in
Bernd Kellner
Goettingen U
Wed, 2010-02-03 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

We introduce p-adic Kummer spaces of continuous functions on $Z_p$ that satisfy certain Kummer type congruences. We will classify these spaces and show their properties, for instance, ring properties and some decompositions. This theory can be transferred to values of Dirichlet L-functions at negative integer arguments in residue classes. That leads to a conjecture about their structure supported by several computations using a link to p-adic functions that are related to Fermat quotients. Finally, we present a conjectural formula of the structure of the classical Bernoulli and Euler numbers.

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