The Ramanujan Journal

, Volume 38, Issue 2, pp 383–422 | Cite as

On a class of functions that satisfies explicit formulae involving the Möbius function

Article
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Abstract

A class of functions that satisfies intriguing explicit formulae of Ramanujan and Titchmarsh involving the zeros of an \(L\)-function in the reduced Selberg class of degree one and its associated Möbius function is studied. Moreover, a sufficient and necessary condition for the truth of the Riemann hypothesis due to Riesz is generalized.

Keywords

Explicit formulae Möbius function Selberg class \(L\)-functions Riemann zeta-function Hankel transformations Special functions 

Mathematics Subject Classification

Primary: 11M06 Secondary: 33C10 
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Notes

Acknowledgments

The authors wish to acknowledge the helpful comments of the referee.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZurichSwitzerland
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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