Zeta functions: Formulas and applications

Journal of Computational and Applied Mathematics

Volumn 118, Issue 1-2, 2000, Pages 125-142

  Elizalde, E ^a,b  

^a INSTITUT D ESTUDIS ESPACIALS DE CATALUNYA IEEC   (Spain)

^b UNIVERSITY OF BARCELONA   (Spain)

Author keywords

11M35; 11M41; 30B40; 30B50; Analytic continuation; Chowla Selberg formula; Determinant; Effective action; Multiplicative anomaly; Zeta function

Indexed keywords

EID: 0001752851     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00284-3     Document Type: Article

References (38)

1. Barnes E.W. Trans. Camb. Phil. Soc. 19:1903;374.
2. Barnes E.W. Trans. Camb. Phil. Soc. 19:1903;426.
3. Bender C.M., Orszag S.A. Advanced Mathematical Methods for Scientists and Engineers. 1978;McGraw-Hill, New York.
4. Bordag M., Elizalde E., Kirsten K., Leseduarte S. Phys. Rev. D. 56:1997;4896.
5. Bousso R., Hawking S.W. Phys. Rev. D. 56:1998;7788.
6. Bytsenko A.A., Williams F.L. J. Math. Phys. 39:1998;1075.
7. Chowla S., Selberg A. Proc. Nat. Acad. Sci. USA. 35:1949;317.
8. Connes A. Noncommutative Geometry. 1994;Academic Press, New York.
9. J.S. Dowker, On the relevance on the multiplicative anomaly hep-th / 9803200, 1998.
10. Elizalde E. J. Phys. A. 22:1989;931.
11. Elizalde E. J. Phys. A. 27:1994;3775.
12. Elizalde E. J. Math. Phys. 31:1990;170.
13. Elizalde E. J. Math. Phys. 35:1994;3308,6100.
14. Elizalde E. Ten Physical Applications of Spectral Zeta Functions. 1995;Springer, Berlin.
15. Elizalde E. J. Phys. A. 30:1997;2735.
16. Elizalde E. Multidimensional extension of the generalized Chowla-Selberg formula. Commun. Math. Phys. 198:1998;83.
17. Elizalde E., Cognola G., Zerbini S. Nucl. Phys. B. 532:1998;407.
18. E. Elizalde, A. Filippi, L. Vanzo, S. Zerbini, Is the multiplicative anomaly dependent on the regularization? hep-th / 9804071, 1998.
19. E. Elizalde, A. Filippi, L. Vanzo, S. Zerbini, Is the multiplicative anomaly relevant? hep-th / 9804072, 1998.
20. Elizalde E., Filippi A., Vanzo L., Zerbini S. Phys. Rev. D. 57:1998;7430.
21. Elizalde E., Odintsov S.D., Romeo A., Bytsenko A.A., Zerbini S. Zeta Regularization Techniques with Applications. 1994;World Scientific, Singapore.
22. Elizalde E., Romeo A. Phys. Rev. D. 40:436;1989.
23. Elizalde E., Vanzo L., Zerbini S. Commun. Math. Phys. 194:1998;613.
24. Epstein P. Math. Ann. 56:1903;615.
25. Epstein P. Math. Ann. 65:1907;205.
26. Evans N. Phys. Lett. B. 457:1999;127.
27. S. Iyanaga, Y. Kawada (Eds.), Encyclopedic Dictionary of Mathematics, Vol. II, MIT Press, Cambridge, MA, 1977, pp. 1372.
28. C. Kassel, Asterisque 177 (1989) 199. Sem. Bourbaki.
29. Kirsten K., Elizalde E. Phys. Lett. B. 365:1995;72.
30. M. Kontsevich, S. Vishik, Functional Analysis on the Eve of the 21st Century, Vol. 1, 1993, pp. 173-197.
31. McKenzie-Smith J.J., Toms D.J. Phys. Rev. D. 58:1998;105 001.
32. Ramond P. Field Theory: a Modern Primer. 1989;Addison-Wesley, Redwood City.
33. Ray D.B. Adv. in Math. 4:1970;109.
34. Ray D.B., Singer I.M. Adv. in Math. 7:1971;145.
35. Ray D.B., Singer I.M. Ann. Math. 98:1973;154.
36. Sachs I., Wipf A. Ann. Phys. (NY). 249:1996;380.
37. Wipf A., Dürr S. Nucl. Phys. B. 443:1995;201.
38. M. Wodzicki, Noncommutative Residue, in: Yu.I. Manin (Ed.), Lecture Notes in Mathematics, Vol. 1289, Springer, Berlin, 1987, p. 320 (Chapter I).