Searching for Kummer congruences in an infinite slope family

Datskovsky, B.; Guerzhoy, P.

doi:10.1090/S0025-5718-03-01608-9

Searching for Kummer congruences in an infinite slope family
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by B. Datskovsky and P. Guerzhoy PDF

Math. Comp. 73 (2004), 861-868 Request permission

Abstract:

We consider powers of a grossencharacter, the corresponding $L$-functions twisted with quadratic Dirichlet characters, and their central critical values. We state several conjectures concerning Kummer-type congruences between these numbers for a ramified prime and describe specific numerical data in support of these conjectures.

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