## Zeta extensions.(English)Zbl 1015.11043

Motivated by some of their earlier unpublished work on analytic properties of higher Selberg zeta functions, the authors formulate problems for general zeta functions with Euler products.

### 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
Full Text:

### Online Encyclopedia of Integer Sequences:

Number of Abelian groups of order n; number of factorizations of n into prime powers.

### 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 [2] Kurokawa, N., and Koyama, S.: Multiple sine functions. Forum. Math. (To appear). · Zbl 1065.11065 [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 [7] Zagier, D.: Zetafunktionen und quadratische körper. Springer-Verlag, Berlin-Heidelberg (1981). · Zbl 0459.10001
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