An integral involving the generalized zeta function. (1990)

• Record Type: Journal Article
• Authors: Elizalde, E.; Romeo, A.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 13:Number 3(1990)
• Page Start: 453
• Page End: 460
• Publication Date: 1990
• Subjects: zeta function -- determinants -- Riemann surfaces -- string theories; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171290000679
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : A general value for∫ a b d t log Γ ( t ), fora, b positive reals, is derived in terms of the Hurwitzζ function. That expression is checked for a previously known special integral, and the case wherea is a positive integer andb is half an odd integer is considered. The result finds application in calculating the numerical value of the derivative of the Riemann zeta function at the point− 1, a quantity that arises in the evaluation of determinants of Laplacians on compact Riemann surfaces.