by E Elizalde (Universitat de Barcelona), S D Odintsov (Universitat de Barcelona), A Romeo (Universitat de Barcelona), A A Bytsenko (Università di Trento), & S Zerbini (Università di Trento)

This book is the result of several years of work by the authors on different aspects of zeta functions and related topics. The aim is twofold. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. Virtually all types of zeta functions are dealt with in the book.

• Riemann and Related Zeta Functions
• Zeta-Function Regularization of Sums Over Known Spectrum
• Zeta Function Regularization Generalized
• The Casimir Effect in Flat Spacetime
• Heat-Kernel and Zeta-Function Regularization Techniques in the Theory of Quantum Fields on Hyperbolic Space
• Quantum Properties of Extended Objects
• Finite-Temperature Effects in Quantum Field Theory
• String Theory at Non-Zero Temperature
• Covariant Effective in 2D Gravity
• Appendix: Calculation of Heat-Kernel Coefficients
• Index