Forbidden conductors of L-functions and continued fractions of particular form

2022/08/27 by Jerzy Kaczorowski, Kaczorowski, J., A. Perelli +3
Mathematics · #11A55 #11M41 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2208.12947

openalex publication_date 2022/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the forbidden values of the conductor q of the L-functions of degree 2 in the extended Selberg class by a novel technique, linking the problem to certain continued fractions and to their weight w_q. Our basic result states that if an L function with conductor q exists, then the weight w_q is unique in a suitable sense. From this we deduce several results, both of theoretical and computational nature.

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