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

Título inglés	An application of Mellin-Barnes type integrals to the mean square of Lerch zeta-functions (II).
Título español	Aplicación de las integrales de tipo Mellin-Barnes a la media cuadrática de funciones zeta de Lerch (II).
Autor/es	Katsurada, Masanori
Organización	Dep. Math. Hiyoshi Camp. Keio Univ., Yokohama, Japón
Revista	0010-0757
Publicación	2005, 56 (1): 57-83, 33 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	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 2 and 3 respectively. In the proofs, Atkinson's method above is enhanced by Mellín-Barnes type of integral formulae (see (4.1)), which further enable us systematic use of various properties of hypergeometric functions (see Section 5); especially in the proof of Theorem 1 crucial roles are played by Lemmas 3 and 5.
Clasificación UNESCO	120502
Palabras clave español	Teoría analítica de números ; Función zeta ; Media cuadrática ; Desarrollo asintótico
Código Z-Math	Zbl 1059.11051
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