Absolute convergence of Ramanujan expansions admits coefficients' coexistence of Ramanujan expansions

2025/02/20 by Giovanni Coppola, Coppola, Giovanni · 1 citation
Mathematics · #11N37 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2502.14415

openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this self-contained short note, we prove that \it every arithmetic function F \it has infinitely many Ramanujan coefficients G \it giving an absolutely convergent Ramanujan expansion for F. This is "coefficients' coexistence": the non-uniqueness, once fixed any F, of these G. They are infinitely many !

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