Eisenstein Series and Convolution Sums

2016/12/29 by Zafer Selçuk Aygin, Aygin, Zafer Selcuk
Mathematics · #11A25 #11E20 #11F11 #11F20 #11F30 #11Y35 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1612.09054

openalex publication_date 2016/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute Fourier series expansions of weight 2 and weight 4 Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums ∑_{a+p b=n}σ(a)σ(b), ∑_{p1a+p2 b=n}σ(a)σ(b) and ∑_{a+p1 p2 b=n}σ(a)σ(b) where p, p₁, p₂ are primes.

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