A generalisation of an identity of Lehmer

• Autorzy: Sanoli Gun , Ekata Saha , Sneh Bala Sinha
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 11J91: Transcendence theory of other special functions
• 11J81: Transcendence (general theory)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 2
• Strony: 121-131

Daty

wydano

2016

Twórcy

autor

Sanoli Gun

• Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai, 600 113, India

autor

Ekata Saha

• The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai, 600 113, India

autor

Sneh Bala Sinha

• Harish-Chandra Research Institute, Jhunsi, 211019 Allahabad, India

Identyfikatory

DOI

10.4064/aa8087-2-2016