May 13, 2024Open Access

Sums of Hurwitz class numbers, CM modular forms, and primes of the form x²+ny²

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Abstract

We consider sums of Hurwitz class numbers of the type ₓ ₌ ₌H (4p-t²), where M is composite. For M=6 and 8, we show that these sums can be expressed in terms of coefficients of CM cusp forms. This leads to explicit formulas which depend on the expression of p in the form x²+ny².

Sums of Hurwitz class numbers, CM modular forms, and primes of the form x²+ny²

Key Points

Abstract

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