Irrationality of the sum of a p-adic series

2017/10/29 by Sílvia Casacuberta, Casacuberta, Sílvia
Mathematics · #11S80 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11S80

paper · pdf · doi:10.48550/arxiv.1710.11484

arxiv created 2017/10/29 · arxiv updated 2017/11/01

Abstract

We prove that the sum of the series ∑_n=0^∞ p^v_p(n!) is a p-adic irrational for all primes p, where v_p(n!) denotes the exponent of the highest power of p dividing n!.

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