Sums involving the Hurwitz zeta function

Ramanujan Journal

Volumn 5, Issue 1, 2001, Pages 5-19

  Kanemitsu, Shigeru ^a   Kumagai, Hiroshi ^c   Yoshimoto, Masami ^b  

^a KINKI UNIVERSITY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

^c NONE

Author keywords

Hurwitz zeta function; Multiple gamma function; Stirling numbers

Indexed keywords

EID: 0035285874     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011496709753     Document Type: Article

References (23)

1. E.W. Barnes, "On the theory of multiple gamma function," Trans. Cambridge Philos. Soc. 19 (1904) 374-425.
2. 3," Math. Japon. 40 (1994) 155-166.
3. J. Choi and H.M. Srivastava, "Sums associated with the zeta function," J. Math. Anal. Appl. 206 (1997) 103-120.
4. J. Choi and H.M. Srivastava, "An application of the theory of the double gamma function," Kyushu J. Math. 53 (1999) 209-222.
5. J. Choi, H.M. Srivastava, and J.R. Quine, "Some series involving the zeta function," Bull. Austral. Math. Soc. 51 (1995) 383-393.
6. L. Comtet, Advanced Combinatorics, D. Reidel Publishing Company, 1974.
7. E. D'Hoker and D.H. Phong, "On the determinants of Laplacians on Riemann surfaces," Comm. Math. Phys. 104 (1986) 537-545.
8. S. Egami, "Reciprocity laws of multiple zeta functions and generalized Dedekind sums," in Analytic Number Theory and Related Topics (K. Nagasaka, ed.), World Scientific, River Edge, 1993, pp. 17-27.
9. S. Kanemitsu, M. Katsurada, and M. Yoshimoto, "On the Hurwitz-Lerch zeta function," Aeq. Math. 59 (2000) 1-19.
10. H. Kumagai, "The determinant of the Laplacian on the n-sphere," Acta Arith. 91 (1999) 199-208.
11. J.R. Quine and J. Choi, "Zeta reguralized products and functional determinants on spheres," Rocky Mountain J. Math. 26 (1996) 719-729.
12. S. Ramanujan, "A series for Euler's constant γ," Messenger Math. 46 (1916-17) 73-80; Collected Papers of Srinivasa Ramanujan, CUP 1927, reprint Chelsea 1962, pp. 163-168.
13. S. Ramanujan, "A series for Euler's constant γ," Messenger Math. 46 (1916-17) 73-80; Collected Papers of Srinivasa Ramanujan, CUP 1927, reprint Chelsea 1962, pp. 163-168.
14. P. Sarnak, "Determinant of Laplacians," Comm. Math. Phys. 110 (1987) 113-120.
15. T. Shintani, "On a Kronecker limit formula for real quadratic fields," J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977) 167-199.
16. T. Shintani, "A proof of the classical Kronecker limit formula," Tokyo J. Math. 3 (1980) 191-199.
17. H.M. Srivastava, "Sums of certain series of the Riemann zeta function," J. Math. Anal. Appl. 134 (1988) 129-140.
18. H.M. Srivastava, "A unified presentation of certain classes of series of the Riemann zeta function," Riv. Mat. Univ. Parma 14 (1988) 1-23.
19. I. Vardi, "Determinants of Laplacians and multiple gamma functions," SIAM J. Math. Anal. 19 (1988) 493-507.
20. M.F. Vignéras, "L'équation fonctionnelle de la fonction zêta de Selberg du groupe modulaire PSL (2, Z)," Astérisque 61 (1979) 235-249.
21. A. Voros, "Spectral functions, special functions and the Selberg zeta function," Comm. Math. Phys. 110 (1987) 439-465.
22. W.I. Weisberger, "Normalization of the path integral measure and the coupling constants for bosonic strings," Nucl. Phys. B284 (1987) 171-200.
23. J.R. Wilton, "A proof of Burnside's formula for log Γ(x + 1 ) and certain allied properties of Riemann's ζ-function," Messenger Math. 52 (1922-23) 90-93.