An algorithm of computing special values of Dwork's p-adic hypergeometric functions in polynomial time

Abstract

Dwork's $p$-adic hypergeometric function is defined to be a ratio ${}_s{F}_{s-1}(t)/{}_s{F}_{s-1}(t^p)$ of hypergeometric power series. Dwork showed that it is a uniform limit of rational functions, and hence one can define special values on $|t{|}_p=1$. However to compute the value modulo $p^n$ in the naive method, the bit complexity increases by exponential when $n\to \infty$. In this paper we present a certain algorithm whose complexity increases at most $O(n^4(\log n{)}^3)$.

38 pages, Introduction is revised

References in corpus (1)

• Dwork crystals I

Cited by in corpus (1)

• Fast evaluation of some p-adic transcendental functions