Displaying similar documents to “Remarks on the upper bound for L(1,χ)”

Kummer congruences for expressions involving generalized Bernoulli polynomials

Glenn J. Fox (2002)

Journal de théorie des nombres de Bordeaux

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We illustrate how a particular expression, involving the generalized Bernoulli polynomials, satisfies systems of congruence relations if and only if a similar expression, involving the generalized Bernoulli numbers, satisfies the same congruence relations. These congruence relations include the Kummer congruences, and recent extensions of the Kummer congruences provided by Gunaratne.

On the generalized Bernoulli numbers that belong to unequal characters.

Ilya Sh. Slavutskii (2000)

Revista Matemática Iberoamericana

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The study of class number invariants of absolute abelian fields, the investigation of congruences for special values of L-functions, Fourier coefficients of half-integral weight modular forms, Rubin's congruences involving the special values of L-functions of elliptic curves with complex multiplication, and many other problems require congruence properties of the generalized Bernoulli numbers (see [16]-[18], [12], [29], [3], etc.). The first steps in this direction can be found in the...