Asymptotic expansions of the mean values of Dirichlet L-functions III.
Linear independence measures for values of Heine series.
Rapidly convergent series representations for ζ(2n+1) and their χ-analogue
Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function
On an asymptotic formula of Ramanujan for a certain theta-type series
Complete asymptotic expansions for certain multiple q-integrals and q-differentials of Thomae-Jackson type
An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions.
We shall establish full asymptotic expansions for the mean squares of Lerch zeta-functions, based on F. V. Atkinson's device. Mellin-Barnes' type integral expression for an infinite double sum will play a central role in the derivation of our main formulae.
An application of Mellin-Barnes type integrals to the mean square of Lerch zeta-functions (II).
For the Lerch zeta-function Φ(s,x,λ) defined below, the multiple mean square of the form (1.1), together with its discrete and Irbid analogues, (1.2) and (1.3) are investigated by means of Atkinson's [2] dissection method applied to the product Φ(u,x,λ)Φ(υ,x,-λ), where u and υ are independent complex variables (see (4.2)). A complete asymptotic expansion of (1.1) as Im s → ±∞ is deduced from Theorem 1, while those of (1.2) and (1.3) as q → ∞ and (at the same time) as Im s → ±∞ are deduced from Theorems...
Asymptotic expansions of the mean values of Dirichlet L-functions.
On Mellin-barnes Type of Integrals and Sumsassociated With the Riemann Zeta-function}
Arithmetical properties of the values of functions satisfying certain functional equations of Poincaré
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