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

2024/05/13 by Mikuláš Zindulka, Zindulka, Mikuláš
Mathematics · #11E41 #11F11 #11F27 #11F37 #11G05 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.07565

openalex publication_date 2024/05/13 · openalex created_date 2024/05/15 · openalex updated_date 2026/07/28

Abstract

We consider sums of Hurwitz class numbers of the type ∑_t ≡ m \pmodMH(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.

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