Absolute convergence of Ramanujan expansions admits coefficients' coexistence of Ramanujan expansions
Abstract
In this self-contained short note, we prove that every arithmetic function F has infinitely many Ramanujan coefficients G 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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