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The joint universality and the functional independence for Lerch zeta-functions

  • Antanas Laurinčikas (a1) and Kohji Matsumoto (a2)

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.

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References

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[2] Bagchi, B., The statistical behaviour and universality properties of the Riemann zeta-function and other allied Dirichlet series, Ph. D. Thesis, Calcutta, Indian Statistical Institute, 1981.
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The joint universality and the functional independence for Lerch zeta-functions

  • Antanas Laurinčikas (a1) and Kohji Matsumoto (a2)

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