A short note on generalized Euler–Briggs constants

Abstract

Recently, Gun, Saha and Sinha had introduced the notion of generalised Euler–Briggs constant [Formula: see text] for a finite set of primes [Formula: see text]. In a subsequent work, Gun, Murty and Saha introduced the following [Formula: see text]-vector space [Formula: see text] and showed that [Formula: see text] In this note, we improve the lower bound, namely [Formula: see text]

On $p$-adic Euler constants

“…The above theorem is different from the one mentioned in [18] as we are not working with (3). With the above theorem, we prove the following: Theorem 3.…”

“…The remaining part of the proof can be carried out along the same lines as [3], Theorem 3. Indeed, we note that as r varies over the primes P, the elements {L p (1, χ) : r ∈ P, χ mod r, χ is non principal, even} are linearly independent over Q. Therefore…”