# A generalisation of an identity of Lehmer

Sanoli Gun; Ekata Saha; Sneh Bala Sinha

Acta Arithmetica (2016)

- Volume: 173, Issue: 2, page 121-131
- ISSN: 0065-1036

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topSanoli Gun, Ekata Saha, and Sneh Bala Sinha. "A generalisation of an identity of Lehmer." Acta Arithmetica 173.2 (2016): 121-131. <http://eudml.org/doc/286513>.

@article{SanoliGun2016,

abstract = {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).},

author = {Sanoli Gun, Ekata Saha, Sneh Bala Sinha},

journal = {Acta Arithmetica},

keywords = {Lehmer identity; baker's theory of linear forms in logarithms; generalised Euler-Briggs constants},

language = {eng},

number = {2},

pages = {121-131},

title = {A generalisation of an identity of Lehmer},

url = {http://eudml.org/doc/286513},

volume = {173},

year = {2016},

}

TY - JOUR

AU - Sanoli Gun

AU - Ekata Saha

AU - Sneh Bala Sinha

TI - A generalisation of an identity of Lehmer

JO - Acta Arithmetica

PY - 2016

VL - 173

IS - 2

SP - 121

EP - 131

AB - 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).

LA - eng

KW - Lehmer identity; baker's theory of linear forms in logarithms; generalised Euler-Briggs constants

UR - http://eudml.org/doc/286513

ER -

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