On Shintani zeta functions for

Author:
Akihiko Yukie

Journal:
Trans. Amer. Math. Soc. **350** (1998), 5067-5094

MSC (1991):
Primary 11M41

DOI:
https://doi.org/10.1090/S0002-9947-98-02050-9

MathSciNet review:
1443897

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider an analogue of the zeta function for not necessarily prehomogeneous representations of and compute some of the poles.

**1.**Datskovsky, B. A mean value theorem for class numbers of quadratic extensions.*Contemporary Mathematics*, 143:179-242, 1993. MR**94m:11137****2.**Datskovsky, B., and D.J. Wright. The adelic zeta function associated with the space of binary cubic forms II: Local theory.*J. Reine Angew. Math.*, 367:27-75, 1986. MR**87m:11034****3.**Datskovsky, B., and D.J. Wright. Density of discriminants of cubic extensions.*J. Reine Angew. Math.*, 386:116-138, 1988. MR**90b:11112****4.**Sato, M., and T. Shintani. On zeta functions associated with prehomogeneous vector spaces.*Ann. of Math.*, 100:131-170, 1974. MR**49:8969****5.**Shintani, T. On Dirichlet series whose coefficients are class-numbers of integral binary cubic forms.*J. Math. Soc. Japan*, 24:132-188, 1972. MR**44:6619****6.**Shintani, T. On zeta-functions associated with vector spaces of quadratic forms.*J. Fac. Sci. Univ. Tokyo, Sect IA*, 22:25-66, 1975. MR**52:5590****7.**Weil, A.*Basic number theory*. Springer-Verlag, Berlin, Heidelberg, New York, 1974. MR**55:302****8.**Wright, D.J. The adelic zeta function associated to the space of binary cubic forms part I: Global theory.*Math. Ann.*, 270:503-534, 1985. MR**86k:11023****9.**Yukie, A. On the Shintani zeta function for the space of binary quadratic forms.*Math. Ann.*, 292:355-374, 1992. MR**93e:11103****10.**Yukie, A.*Shintani zeta functions*, volume 183 of*London Math. Soc. Lecture Note Series*. Cambridge University Press, Cambridge, 1993. MR**95h:11037**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (1991):
11M41

Retrieve articles in all journals with MSC (1991): 11M41

Additional Information

**Akihiko Yukie**

Affiliation:
Department of Mathematics, Oklahoma State University, 401 Math Science, Stillwater, Oklahoma 74078-1058

Email:
yukie@math.okstate.edu

DOI:
https://doi.org/10.1090/S0002-9947-98-02050-9

Received by editor(s):
August 28, 1995

Received by editor(s) in revised form:
January 29, 1997

Additional Notes:
The author was partially supported by NSF

Article copyright:
© Copyright 1998
American Mathematical Society