Equidistribution of Heegner points and the partition function Academic Article uri icon

abstract

  • Let p(n) denote the number of partitions of a positive integer n. In this paper we study the asymptotic growth of p(n) using the equidistribution of Galois orbits of Heegner points on the modular curve X0(6). We obtain a new asymptotic formula for p(n) with an effective error term which is O(n-(1/2+)) for some > 0. We then use this asymptotic formula to sharpen the classical bounds of Hardy and Ramanujan, Rademacher, and Lehmer on the error term in Rademacher's exact formula for p(n). 2010 Springer-Verlag.

published proceedings

  • Mathematische Annalen

author list (cited authors)

  • Folsom, A., & Masri, R.

citation count

  • 14

publication date

  • October 2010