A generalized Euler-Maclaurin formula for the Hurwitz zeta function

Eugenio P. Balanzario

Displaying similar documents to “A generalized Euler-Maclaurin formula for the Hurwitz zeta function”

An application of Mellin-Barnes' type integrals to the mean square of Lerch zeta-functions.

Masanori Katsurada (1997)

Collectanea Mathematica

Similarity:

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.

On Epstein's zeta function

Paul Bateman, E. Grosswald (1964)

Acta Arithmetica

Similarity:

On Ramanujan's formula for values of Riemann zeta-function at positive odd integers

Koji Katayama (1973)

Acta Arithmetica

Similarity:

On mean values of some zeta-functions in the critical strip

Aleksandar Ivić (2003)

Journal de théorie des nombres de Bordeaux

Similarity:

For a fixed integer $k \geq 3$ , and fixed $\frac{1}{2} < σ < 1$ we consider $\int_{1}^{T} {|ζ (σ + i t)|}^{2 k} d t = \sum_{n = 1}^{\infty} d_{k}^{2} (n) n^{- 2 σ} T + R (k, σ; T),$ where $R (k, σ; T) = 0 (T) (T \to \infty)$ is the error term in the above asymptotic formula. Hitherto the sharpest bounds for $R (k, σ; T)$ are derived in the range min $(β_{k}, σ_{k}^{*}) < σ < 1$ . We also obtain new mean value results for the zeta-function of holomorphic cusp forms and the Rankin-Selberg series.

A Note on the Hurwitz Zeta Function

Đurđe Cvijović, Jacek Klinowski (2000)

Matematički Vesnik

Similarity:

A relation between the Riemann zeta-function and the hyperbolic laplacian

Yoichi Motohashi (1995)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Zeta functions for the Riemann zeros

André Voros (2003)

Annales de l’institut Fourier

Similarity:

A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.