Note on the Zeros of a Dirichlet Function
L. Ferry
The Green Weasenham, Kings Lynn, Norfolk, PE32 2TD, United Kingdom.
D. Ghisa *
Department of Mathematics, York University, Glendon College, 2275 Bayview Avenue, Toronto, On, M4N 3M6, Canada.
F. A. Muscutar
Department of Science and Mathematics, Lorain CCC, 1005 Abbe Road, Elyria, OH 44035, USA.
*Author to whom correspondence should be addressed.
Abstract
The existence of non trivial zeros off the critical line for a function obtained by analytic continuation of a particular Dirichlet series is studied. Our findings are in contradiction with some results of computations which were present in the field for a long time. In the first part of this note, we illustrate how the approximation errors may have had as effect inexact conclusions and in the second part we prove rigorously our point of view.
Keywords: Dirichlet character, Dirichlet L-function, non trivial zero, critical line