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arXiv · 1909.03649

On complex explicit formulae connected with the M\"obius function of an elliptic curve

Adrian Łydka
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Abstract

We study analytic properties function $m(z, E)$, which is defined on the upper half-plane as an integral from the shifted $L$-function of an elliptic curve. We show that $m(z, E)$ analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for $m(z, E)$ in the strip $|\Im{z}|<2\pi$.

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Adrian Łydka. 2019-09-09. On complex explicit formulae connected with the M\"obius function of an elliptic curve. https://arxiv.org/abs/1909.03649

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