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Sums of class numbers and mixed mock modular forms

  • KATHRIN BRINGMANN (a1) and BEN KANE (a2)

Abstract

In this paper, we consider sums of class numbers of the type ∑ma (mod p) H (4nm2), where p is an odd prime, n ∈ ℕ, and a ∈ ℤ. By showing that these are coefficients of mixed mock modular forms, we obtain explicit formulas. Using these formulas for p = 5 and 7, we then prove a conjecture of Brown et al. in the case that n = ℓ is prime.

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The research of the first author was supported by the Alfried Krupp Prize for Young University Teachers of the Krupp Foundation.

This research was completed while the second author was a postdoc at the University of Cologne.

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References

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Sums of class numbers and mixed mock modular forms

  • KATHRIN BRINGMANN (a1) and BEN KANE (a2)

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