most recent 30 from http://mathoverflow.net 2013-06-19T17:07:18Z http://mathoverflow.net/feeds/question/52534 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/52534/picard-fuchs-and-lefschetz-trace Jill 2011-01-19T17:23:03Z 2011-01-19T17:23:03Z

<p>In Clemen's book "A Scrapbook of Complex Curve Theory", he discusses in Chapter 2 how the infinite sum giving the period of the Legendre curve matches (mod p) the sum giving the number of points over that same curve in F_p. He then describes in the section "the unity of mathematics" why this is so, using Lefschetz fixed point theorem.</p> <p>However, this section is very brief, and I was hoping to understand it better. Are there any other good references that you know of? I am trying to understand this connection between the number of points over a finite field for an arbitrary elliptic curve and Picard-Fuchs.</p> <p>Thanks!</p>