Partitions into Distinct Parts and Elliptic Curves

Abstract

LetQ(N) denote the number of partitions ofNinto distinct parts. Ifω(k):=(3k2+k)/2, then it is well known that[formula]In this short note we start with Tunnell's work on the "congruent number problem" and show thatQ(N) often satisfies "weighted" recurrence type relations. For everyNthere is a relation forQ(N) which may involve a special value of an elliptic curveL-function. © 1998 Academic Press.