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Motivated by some of their earlier unpublished work on analytic properties of higher Selberg zeta functions, the authors formulate problems for general zeta functions with Euler products.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