Gamma-function analogues for Gauss sums - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T06:41:17Z http://mathoverflow.net/feeds/question/83930 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83930/gamma-function-analogues-for-gauss-sums Gamma-function analogues for Gauss sums diana 2011-12-20T10:51:21Z 2011-12-20T12:48:22Z <p>I have an Gauss sum, which I have to colculate I have heard that it has an analogues form with the Gumma function, but couldn't find its formular shape. It would be so nice of you to help me and write the mathematical shape of the link between these two funktions. Beforehand thank you.</p> http://mathoverflow.net/questions/83930/gamma-function-analogues-for-gauss-sums/83937#83937 Answer by Igor Rivin for Gamma-function analogues for Gauss sums Igor Rivin 2011-12-20T12:19:29Z 2011-12-20T12:19:29Z <p>See <a href="http://dml.cz/dmlcz/701518" rel="nofollow">http://dml.cz/dmlcz/701518</a> Very lucid and freely available.</p> http://mathoverflow.net/questions/83930/gamma-function-analogues-for-gauss-sums/83938#83938 Answer by Eric Naslund for Gamma-function analogues for Gauss sums Eric Naslund 2011-12-20T12:36:01Z 2011-12-20T12:48:22Z <p>The connection between Gauss sums and the \$p\$-adic Gamma function is a very deep theorem, and given by the <a href="http://en.wikipedia.org/wiki/Gross%E2%80%93Koblitz_formula" rel="nofollow">Gross-Koblitz formula</a>. </p> <p>Here is the original paper by Gross and Koblitz: <a href="http://www.jstor.org/pss/1971226" rel="nofollow">Gauss sums and the \$p\$-adic \$\Gamma\$-function. (1979)</a></p> <p>For some more specific cases and applications, see the book by Berndt, Evans, and Williams, "Gauss and Jacobi Sums. (1998)"</p>