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Independence of Artin L-functions

  • Mircea Cimpoeaş and Florin Nicolae EMAIL logo
Published/Copyright: November 13, 2018

Abstract

Let K/ be a finite Galois extension. Let χ1,,χr be r1 distinct characters of the Galois group with the associated Artin L-functions L(s,χ1),,L(s,χr). Let m0. We prove that the derivatives L(k)(s,χj), 1jr, 0km, are linearly independent over the field of meromorphic functions of order <1. From this it follows that the L-functions corresponding to the irreducible characters are algebraically independent over the field of meromorphic functions of order <1.

MSC 2010: 11R42; 11M41

Communicated by Freydoon Shahidi


References

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Received: 2018-08-08
Revised: 2018-10-15
Published Online: 2018-11-13
Published in Print: 2019-03-01

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