most recent 30 from http://mathoverflow.net 2013-06-20T09:24:51Z http://mathoverflow.net/feeds/question/95815 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95815/p-adic-analysis-of-hypergeometric-functions Kale 2012-05-02T22:57:28Z 2012-05-03T04:53:53Z

<p>Are there any p-adic techniques that can be applied to the 2F1 hypergeometric function?</p> <p>For e.g. I'm interested in which values this function converges p-adically.</p>

http://mathoverflow.net/questions/95815/p-adic-analysis-of-hypergeometric-functions/95825#95825 Anatoly Kochubei 2012-05-03T04:53:53Z 2012-05-03T04:53:53Z

<p>The Gauss hypergeometric function is the main example in the theory of p-adic differential equations. See </p> <p>K. S. Kedlaya, p-Adic Differential Equations, Cambridge University Press, 2010,</p> <p>for the general theory. There were also two books by Dwork, almost completely devoted to ${}_2F_1$ (its p-adic theory is much more complicated than the classical one):</p> <p>B. Dwork, Generalized hypergeometric functions. Oxford: Clarendon Press, 1990. </p> <p>B. Dwork, Lectures on p-adic differential equations, Springer, 1982.</p> <p>It is easy to check local p-adic convergence for the hypergeometric series, but to study and even correctly define its analytic continuation properties one needs subtle analytic and algebraic techniques.</p>