Algebraic relations between special values of multiple sine functions
Algebraic setup of non-strict multiple zeta values
An alternative approach to a theorem of Tom Meurman
An Alternative Form of the Functional Equation for Riemann’s Zeta Function, II
This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for . We present here, after showing the first proof of Riemann, a new, simple and direct proof of the symmetric form of the functional equation for both the Eulerian Zeta function and the alternating Zeta function, connected with odd numbers. A proof that Euler himself could have arranged with a little step at the end of his paper “Remarques sur un beau rapport entre...
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...
An application of the Hooley-Huxley contour
An approach to zeta-function of finite factorgraph via the Markov topological chains
An arithmetical mapping and applications to Ω-results for the Riemann zeta function
An Asymptotic Formula for a sum Involving Zeros of the Riemann Zeta-function
An Asymptotic Formula in the Theory of Numbers.
An Asymptotic Formula in the Theory of Numbers. II:
An Asymptotic Formula in the Theory of Numbers. III.
An asymptotic formula relating the Siegel zero and the class number of quadratic fields
An asymptotic inequality concerning primes in contours for the case of quadratic number fields
An asymptotic series for the mean value of Dirichlet L-functions.
An average formula for the class number
An effective order of Hecke-Landau zeta functions near the line σ=1, II (some applications)
An effective order of Hecke-Landau zeta functions near the line σ = 1. I
An elementary treatment of a general diophantine problem