Arithmetic hypergeometric series

W. Zudilin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 2, pp. 369-420

Résumé

The main goal of this survey is to give common characteristics of auxiliary hypergeometric functions (and their generalisations), functions which occur in number-theoretic problems. Originally designed as a tool for solving these problems, the hypergeometric series have become a connecting link between different areas of number theory and mathematics in general. Bibliography: 183 titles.

Détail

Keywords: hypergeometric series, zeta value, Ramanujan's mathematics, irrationality measure, modular form, Calabi–Yau differential equation, Mahler measure, Wilf–Zeilberger theory, algorithm of creative telescoping.
Mots-clés : Diophantine approximation

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