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A generalisation of an identity of Lehmer

Sanoli Gun, Ekata Saha, Sneh Bala Sinha (2016)

Acta Arithmetica

We prove an identity involving generalised Euler-Briggs constants, Euler's constant, and linear forms in logarithms of algebraic numbers. This generalises and gives an alternative proof of an identity of Lehmer (1975). Further, this identity facilitates the investigation of the (conjectural) transcendental nature of generalised Euler-Briggs constants. Earlier investigations of similar type by the present authors involved the interplay between additive and multiplicative characters. This in turn...

A note on the transcendence of infinite products

Jaroslav Hančl, Ondřej Kolouch, Simona Pulcerová, Jan Štěpnička (2012)

Czechoslovak Mathematical Journal

The paper deals with several criteria for the transcendence of infinite products of the form n = 1 [ b n α a n ] / b n α a n where α > 1 is a positive algebraic number having a conjugate α * such that α | α * | > 1 , { a n } n = 1 and { b n } n = 1 are two sequences of positive integers with some specific conditions. The proofs are based on the recent theorem of Corvaja and Zannier which relies on the Subspace Theorem (P. Corvaja, U. Zannier: On the rational approximation to the powers of an algebraic number: solution of two problems of Mahler and Mendès France, Acta...

A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function

M. C. Lettington (2013)

Acta Arithmetica

We study the interplay between recurrences for zeta related functions at integer values, 'Minor Corner Lattice' Toeplitz determinants and integer composition based sums. Our investigations touch on functional identities due to Ramanujan and Grosswald, the transcendence of the zeta function at odd integer values, the Li Criterion for the Riemann Hypothesis and pseudo-characteristic polynomials for zeta related functions. We begin with a recent result for ζ(2s) and some seemingly new Bernoulli relations,...

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