Zeta extensions. (English) Zbl 1015.11043

Kurokawa, Nobushige; Wakayama, Masato

Proc. Japan Acad., Ser. A 78, No. 7, 126-130 (2002).

Motivated by some of their earlier unpublished work on analytic properties of higher Selberg zeta functions, the authors formulate problems for general zeta functions with Euler products.

Reviewer: Tom M.Apostol (Pasadena)

MSC:

11M36	Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)
11M41	Other Dirichlet series and zeta functions

Keywords:

general zeta functions with Euler products

References:

[1]	Cohen, H., and Lenstra, H. W.: Heuristics on class groups of number fields. Lecture Notes in Math., no.,1068, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, pp. 33-62 (1984). · Zbl 0558.12002 · doi:10.1007/BFb0099440
[2]	Kurokawa, N., and Koyama, S.: Multiple sine functions. Forum. Math. (To appear). · Zbl 1065.11065 · doi:10.1515/form.2003.042
[3]	Kurokawa, N., Ochiai, H., and Wakayama, M.: Zetas and multiple trigonometry. J. Ramanujan Math. Soc., 17 , 101-113 (2002). · Zbl 0995.11054
[4]	Kurokawa, N., and Wakayama, M.: On \(\zeta(3)\). J. Ramanujan Math. Soc., 16 , 205-214 (2001). · Zbl 1014.11049
[5]	Kurokawa, N., and Wakayama, M.: A comparison between the sum over Selberg’s zeroes and Riemann’s zeroes. (2002). (Preprint). · Zbl 1114.11307
[6]	Kurokawa, N., and Wakayama, M.: Higher Selberg zeta functions. (2002). (Preprint). · Zbl 1060.11050 · doi:10.1007/s00220-004-1065-z
[7]	Zagier, D.: Zetafunktionen und quadratische körper. Springer-Verlag, Berlin-Heidelberg (1981). · Zbl 0459.10001