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Research Article Open access CC BY 4.0

On Davenport and Heilbronn-Type of Functions

L. Ferry, D. Ghisa, F. A. Muscutar

Journal of Advances in Mathematics and Computer Science · pp. 1–7 · Published 15 Mar 2016

10.9734/BJMCS/2016/24648

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.

Dirichlet character Dirichlet L-function non trivial zero critical line

References (8)

  1. 1 Multiplicative Number Theory [DOI]
  2. 2 Multiplicative Number Theory I: Classical Theory
  3. 3 Around the Davenport-Heilbronn function [DOI]
  4. 4 Zeros of the Davenport-Heilbronn counterexample [DOI]
  5. 5 The Zeros of Epstein's Zeta-Functions [DOI]
  6. 6 Some Zeros of the Titchmarsh Counterexample [DOI]
  7. 7 Fundamental Domains and Analytic Continuation of General Dirichlet Series [DOI]
  8. 8 On the generalized Riemann hypothesis II [DOI]

Cited by 2

On The Generalized Riemann Hypothesis II

· International Journal of Scientific and Innovative Mathematical Research · 2016

On the generalized Riemann hypothesis II

Dorin Ghişa · arXiv (Cornell University) · 2016

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