I am with the following problem.
There is a closed formula or some lower bound for the $p$-adic valuation of the product $\prod_{k=1}^m(a+k\ell)$ (Pochhammer symbol)? where $a$ and $\ell$ are positive integers.
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.
Sign up to join this communityI am with the following problem.
There is a closed formula or some lower bound for the $p$-adic valuation of the product $\prod_{k=1}^m(a+k\ell)$ (Pochhammer symbol)? where $a$ and $\ell$ are positive integers.
See Chapter 5, "The $p$-adic evaluation of Pochhammer symbols", in On Dwork’s $p$-adic formal congruences theorem and hypergeometric mirror maps by E. Delaygue, T. Rivoal and J. Roques, Memoirs of the American Mathematical Society 246, 1163 (2017). [A preprint from 2013 has open access here, see page 22.