Singular moduli and the distribution of partition ranks modulo 2 Academic Article uri icon

abstract

  • Copyright © Cambridge Philosophical Society 2015. In this paper, we prove an asymptotic formula with a power saving error term for traces of weight zero weakly holomorphic modular forms of level N along Galois orbits of Heegner points on the modular curve X0(N). We use this result to study the distribution of partition ranks modulo 2. In particular, we give an asymptotic formula with a power saving error term for the number of partitions of a positive integer n with even (respectively, odd) rank. We use these results to deduce a strong quantitative form of equidistribution of partition ranks modulo 2.

author list (cited authors)

  • MASRI, R.

citation count

  • 3

complete list of authors

  • MASRI, RIAD

publication date

  • December 2015