Fourier Coefficients of Beurling Functions and a Class of Mellin Transform Formally Determined by its Values on the Even Integers

2004/07/27 by F. Auil, Fernando Auil, Auil, F.
Mathematics · #Algebraic and Geometric Analysis #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0407466

arxiv created 2004/07/27 · openalex publication_date 2004/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is a well-known fact that Riemann Hypothesis will follows if the function identically equal to -1 can be arbitrarily approximated in the norm \norma. of L²([0,1],dx) by functions of the form f(x)=∑_k=1ⁿa_k ρ(\fracθ_kx), where ρ(x)\adef\pfracx, and a_k∈\cc, 0

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