Mellin transform techniques for zeta-function resummations

نویسندگان

  • E. Elizalde
  • S. Zerbini
چکیده

Making use of inverse Mellin transform techniques for analytical continuation, an elegant proof and an extension of the zeta function regularization theorem is obtained. No series commutations are involved in the procedure; nevertheless the result is naturally split into the same three contributions of very different nature, i.e. the series of Riemann zeta functions and the power and negative exponentially behaved functions, respectively, well known from the original proof. The new theorem deals equally well with elliptic differential operators whose spectrum is not explicitly known. Rigorous results on the asymptoticity of the outcoming series are given, together with some specific examples. Exact analytical formulas, simplifying approximations and numerical estimates for the last of the three contributions (the most difficult to handle) are obtained. As an application of the method, the summation of the series which appear in the analytic computation (for different ranges of temperature) of the partition function of the string —basic in order to ascertain if QCD is some limit of a string theory— is performed. 1 E-mail address: eli @ ebubecm1.bitnet

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

GENERAL SOLUTION OF ELASTICITY PROBLEMS IN TWO DIMENSIONAL POLAR COORDINATES USING MELLIN TRANSFORM

Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic  ...

متن کامل

The Modified Mellin Transform of Powers of the Zeta-function

The modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) is investigated. Analytic continuation and mean square estimates of Zk(s) are discussed, as well as connections with power moments of |ζ( 1 2 +ix)|, with the special emphasis on the cases k = 1, 2.

متن کامل

Appendix. the Mellin Transform and Related Analytic Techniques

The Mellin transformation is a basic tool for analyzing the behavior of many important functions in mathematics and mathematical physics, such as the zeta functions occurring in number theory and in connection with various spectral problems. We describe it first in its simplest form and then explain how this basic definition can be extended to a much wider class of functions, important for many...

متن کامل

A (p, V )-extension of Hurwitz-lerch Zeta Function and Its Properties

In this paper, we define a (p, v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results. keywords...

متن کامل

Certain Results Involving a Class of Functions Associated with the Hurwitz Zeta Function

Abstract. The purpose of this paper is to consider a new generalization of the Hurwitz zeta function. Generating functions, Mellin transform, and a series identity are obtained for this generalized class of functions. Some of the results are used to provide a further generalization of the Lambert transform. Relevance with various known results are depicted invariably. Multivariable extensions a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1993