JEDNOSTKA NAUKOWA KATEGORII A+

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

Tom 210 / 2023

Jerzy Kaczorowski, Alberto Perelli, Maciej Radziejewski Acta Arithmetica 210 (2023), 1-21 MSC: Primary 11M41; Secondary 11A55. DOI: 10.4064/aa220721-30-9 Opublikowany online: 26 October 2023

Streszczenie

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.

Published in Open Access (under CC-BY license).

Autorzy

  • Jerzy KaczorowskiFaculty of Mathematics and Computer Science
    Adam Mickiewicz University, Poznań
    61-614 Poznań, Poland
    and
    Institute of Mathematics
    Polish Academy of Sciences
    00-656 Warszawa, Poland
    e-mail
  • Alberto PerelliDipartimento di Matematica
    Università di Genova
    via Dodecaneso 35
    16146 Genova, Italy
    e-mail
  • Maciej RadziejewskiFaculty of Mathematics and Computer Science
    Adam Mickiewicz University, Poznań
    61-614 Poznań, Poland
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek