On Davenport and Heilbronn-Type of Functions
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
A correction is brought to the opinion expressed in a previous note that the off critical line points indicated as being non trivial zeros of Davenport and Heilbronn function are affected of approximation errors and illustrations are presented which enforce the conclusion that they are true zeros. It is shown also that linear combinations of L-functions satisfying the same Riemann-type of functional equation do not offer counterexamples to RH, contrary to a largely accepted position.
Keywords: Dirichlet character, Dirichlet L-function, non trivial zero, critical line