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On Complex Explicit Formulae Connected with the Möbius Function of an Elliptic Curve
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 2 / 14 June 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 381-389
- Print publication:
- 14 June 2014
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- Article
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We study analytic properties function
$m\left( z,\,E \right)$, which is defined on the upper half-plane as an integral from the shifted 
$L$-function of an elliptic curve. We show that $m\left( z,\,E \right)$ analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for $m\left( z,\,E \right)$ in the strip 
$\left| \Im z \right|\,<\,2\pi$.
