Author:
Laurinčikas Antanas,Matsumoto Kohji
Abstract
The joint universality theorem for Lerch zeta-functions L(λl, αl, s) (1 ≤ l ≤ n) is proved, in the case when λls are rational numbers and αls are transcendental numbers. The case n = 1 was known before ([12]); the rationality of λls is used to establish the theorem for the “joint” case n ≥ 2. As a corollary, the joint functional independence for those functions is shown.
Publisher
Cambridge University Press (CUP)
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4. Note sur la fonction
$\mathfrak{K}(w, x, s) = \sum\limits_{k = 0}^\infty {\frac{{e^{2k\pi ix} }}{{\left( {w + k} \right)^3 }}} $
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