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

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: hypergeometric series, zeta value, Ramanujan's mathematics, Diophantine approximation, irrationality measure, modular form, Calabi–Yau differential equation, Mahler measure, Wilf–Zeilberger theory, algorithm of creative telescoping. 
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     author = {W. Zudilin},
     title = {Arithmetic hypergeometric series},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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W. Zudilin. Arithmetic hypergeometric series. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 2, pp. 369-420. http://geodesic.mathdoc.fr/item/RM_2011_66_2_a3/