most recent 30 from http://mathoverflow.net 2013-05-20T22:34:42Z http://mathoverflow.net/feeds/question/113962 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/113962/a-rapidly-converging-series-of-the-hasseweil-l-function-associated-with-an-ellip RH 2012-11-20T16:30:10Z 2012-11-20T17:39:22Z

<p>I know that for some L-series there is still a rapidly-converging series. My question is about the existence of a such a series for the Dirichlet series of the Hasse–Weil L-function associated with an elliptic curve over rationals. A google search do not gives important answers. </p>

http://mathoverflow.net/questions/113962/a-rapidly-converging-series-of-the-hasseweil-l-function-associated-with-an-ellip/113966#113966 Denis Chaperon de Lauzières 2012-11-20T17:39:22Z 2012-11-20T17:39:22Z

<p>Possibly the answer would be the so-called "approximate functional equation" for the $L$-function. This of course takes as input the modularity of the Hasse-Weil zeta function, and gives rapidly convergent series representing it at any point. I would expect Cremona's book on algorithms for modular elliptic curves to contain a description. Software like Pari/GP implements such algorithms (see the command elllseries).</p>