Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

The Deuring-Heilbronn Phenomenon for Artin L-functions


Affiliations
1 Department of Mathematics, University of Toronto, 100 St. George Street, Toronto, Ontario, M5S 3G3, Canada
     

   Subscribe/Renew Journal


Let E/K be a Galois extension of number fields with group G, and let x be a character of G. The goal of this note is to establish a version of the Deuring-Heilbronn Phenomenon (DHP) for non-Abelian Artin L-functions L(s,x,E/K) under the assumption of Artin's conjecture. The phenomenon, first observed for Dirichlet L-functions, is the fact that a zero of the L-function very close to s = 1 has the effect of pushing the other zeros away from the line σ = 1. In [1] a version of DHP for (K(S) has been proved. Here we generalize that result to non-Abelian L-functions.
User
Subscription Login to verify subscription
Notifications
Font Size


  • The Deuring-Heilbronn Phenomenon for Artin L-functions

Abstract Views: 310  |  PDF Views: 0

Authors

Kambiz Mahmoudian
Department of Mathematics, University of Toronto, 100 St. George Street, Toronto, Ontario, M5S 3G3, Canada

Abstract


Let E/K be a Galois extension of number fields with group G, and let x be a character of G. The goal of this note is to establish a version of the Deuring-Heilbronn Phenomenon (DHP) for non-Abelian Artin L-functions L(s,x,E/K) under the assumption of Artin's conjecture. The phenomenon, first observed for Dirichlet L-functions, is the fact that a zero of the L-function very close to s = 1 has the effect of pushing the other zeros away from the line σ = 1. In [1] a version of DHP for (K(S) has been proved. Here we generalize that result to non-Abelian L-functions.