1Institute of Mathematical Sciences C.I.T. Campus, Taramani Chennai, 600 113, India 2The Institute of Mathematical Sciences C.I.T. Campus, Taramani Chennai, 600 113, India 3Harish-Chandra Research Institute, Jhunsi 211019 Allahabad, India
Acta Arithmetica, Tome 173 (2016) no. 2, pp. 121-131
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 rendered inevitable a careful analysis of multiplicatively independent units in suitable cyclotomic fields. The generalised Lehmer identity derived here avoids this, leading to natural and transparent proofs of earlier results. It also allows us to prove a stronger result (see Corollary 2).
Keywords:
prove identity involving generalised euler briggs constants euler constant linear forms logarithms algebraic numbers generalises gives alternative proof identity lehmer further identity facilitates investigation conjectural transcendental nature generalised euler briggs constants earlier investigations similar type present authors involved interplay between additive multiplicative characters turn rendered inevitable careful analysis multiplicatively independent units suitable cyclotomic fields generalised lehmer identity derived here avoids leading natural transparent proofs earlier results allows prove stronger result see corollary nbsp
Affiliations des auteurs :
Sanoli Gun
1
;
Ekata Saha
2
;
Sneh Bala Sinha
3
1
Institute of Mathematical Sciences C.I.T. Campus, Taramani Chennai, 600 113, India
2
The Institute of Mathematical Sciences C.I.T. Campus, Taramani Chennai, 600 113, India
3
Harish-Chandra Research Institute, Jhunsi 211019 Allahabad, India
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author = {Sanoli Gun and Ekata Saha and Sneh Bala Sinha},
title = {A generalisation of an identity of {Lehmer}},
journal = {Acta Arithmetica},
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doi = {10.4064/aa8087-2-2016},
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Sanoli Gun; Ekata Saha; Sneh Bala Sinha. A generalisation of an identity of Lehmer. Acta Arithmetica, Tome 173 (2016) no. 2, pp. 121-131. doi: 10.4064/aa8087-2-2016
