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

Kühn, Patrick; Robles, Nicolas; Roy, Arindam (2015). On a class of functions that satisfies explicit formulae involving the Möbius function. The Ramanujan Journal, 38(2):383-422.

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.

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.

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