Displaying similar documents to “Enumerating non-equivalent matrices over principal ideal domains”

On Bernoulli identities and applications.

Minking Eie, King F. Lai (1998)

Revista Matemática Iberoamericana

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Bernoulli numbers appear as special values of zeta functions at integers and identities relating the Bernoulli numbers follow as a consequence of properties of the corresponding zeta functions. The most famous example is that of the special values of the Riemann zeta function and the Bernoulli identities due to Euler. In this paper we introduce a general principle for producing Bernoulli identities and apply it to zeta functions considered by Shintani, Zagier and Eie. Our results include...

Well-poised hypergeometric service for diophantine problems of zeta values

Wadim Zudilin (2003)

Journal de théorie des nombres de Bordeaux

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It is explained how the classical concept of well-poised hypergeometric series and integrals becomes crucial in studying arithmetic properties of the values of Riemann’s zeta function. By these well-poised means we obtain: (1) a permutation group for linear forms in 1 and ζ ( 4 ) = π 4 / 90 yielding a conditional upper bound for the irrationality measure of ζ ( 4 ) ; (2) a second-order Apéry-like recursion for ζ ( 4 ) and some low-order recursions for linear forms in odd zeta values; (3) a rich permutation group...