Irrationality of the sum of a $p$-adic series

Sílvia Casacuberta

We prove that the sum of the series ${\sum }_{n=0}^{\infty }{p}^{v_p(n!)}$ is a $p$-adic irrational for all primes $p$, where $v_p(n!)$ denotes the exponent of the highest power of $p…