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.
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$\begingroup$ please don't crosspost, to avoid duplication of efforts --- math.stackexchange.com/questions/2152795/… $\endgroup$– Carlo BeenakkerCommented Feb 20, 2017 at 13:25
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1 Answer
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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.
answered Feb 20, 2017 at 13:32
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$\begingroup$ DO you have this book? I don't have access to it. Thanks in advance! $\endgroup$ Commented Feb 20, 2017 at 13:39
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$\begingroup$ I can't access. It ask username and password. $\endgroup$ Commented Feb 20, 2017 at 13:43
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$\begingroup$ I found, but it is only for $\ell=1$ $\endgroup$ Commented Feb 20, 2017 at 13:46