A generalisation of an identity of Lehmer

Gun, Sanoli; Saha, Ekata; Sinha, Sneh Bala

doi:10.4064/aa8087-2-2016

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“…The last equality has been established by Diamond and Ford in [4]. In a recent work, the first and the third author along with Sneh Bala Sinha [6] (see also [7]) proved the following results; Then the set T := {γ(Ω, a, q) | Ω ∈ U } is infinite and has at most one algebraic element.…”

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confidence: 89%

“…The articles [6,7] can be thought of a generalization of the work of R. Murty and Zaytseva [17] on generalized Euler constants. Whereas the results of R. Murty and Zaytseva are obtained by Hermite and Lindemann theorem, the proofs in [6] require careful analysis of units in cyclotomic fields and Baker's theorem on linear forms in logarithms.…”

Section: Theorem 4 (Gun Saha and Sinha)mentioning

confidence: 99%

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Linear and algebraic independence of generalized Euler–Briggs constants

Gun

Murty

Saha

2016

Journal of Number Theory

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ABSTRACT. Possible transcendental nature of Euler's constant γ has been the focus of study for sometime now. One possible approach is to consider γ not in isolation, but as an element of the infinite family of generalised Euler-Briggs constants. In a recent work [6], it is shown that the infinite list of generalized Euler-Briggs constants can have at most one algebraic number. In this paper, we study the dimension of spaces generated by these generalized Euler-Briggs constants over number fields. More precisely, we obtain non-trivial lower bounds (see Theorem 5 and Theorem 6) on the dimension of these spaces and consequently establish the infinite dimensionality of the space spanned. Further, we study linear and algebraic independence of these constants over the field of all algebraic numbers.

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confidence: 89%