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Equidistribution of Heegner points and the partition function

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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 X 0(6). We obtain a new asymptotic formula for p(n) with an effective error term which is \({O(n^{-(\frac{1}{2}+\delta)})}\) for some δ > 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).

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  1. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Amanda Folsom & Riad Masri

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  1. Amanda Folsom
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  2. Riad Masri
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Correspondence to Riad Masri.

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Folsom, A., Masri, R. Equidistribution of Heegner points and the partition function. Math. Ann. 348, 289–317 (2010). https://doi.org/10.1007/s00208-010-0478-6

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  • DOI: https://doi.org/10.1007/s00208-010-0478-6

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