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On Popov's explicit formula and the Davenport expansion

Quan YangJay MehtaShigeru Kanemitsu — 2023

Czechoslovak Mathematical Journal

We shall establish an explicit formula for the Davenport series in terms of trivial zeros of the Riemann zeta-function, where by the Davenport series we mean an infinite series involving a PNT (Prime Number Theorem) related to arithmetic function a n with the periodic Bernoulli polynomial weight B ¯ ϰ ( n x ) and PNT arithmetic functions include the von Mangoldt function, Möbius function and Liouville function, etc. The Riesz sum of order 0 or 1 gives the well-known explicit formula for respectively the partial...

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