Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On Shintani zeta functions for $\mathrm{GL}(2)$

Author: Akihiko Yukie
Journal: Trans. Amer. Math. Soc. 350 (1998), 5067-5094
MSC (1991): Primary 11M41
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 $\text{GL}(2)$ and compute some of the poles.

References [Enhancements On Off] (What's this?)

  • 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

Similar Articles

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

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

American Mathematical Society