|
On the exact location of the zeros of certain families of rational period functions and other related rational functions
Author(s):
Ellen
Gethner
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1-10.
MSC (1991):
Primary 11F99
MathSciNet review:
1622750
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
The classification of Rational Period Functions on the modular group has been of some interest recently, and was accomplished by studying the pole sets of these rational functions. We take a complex analytic point of view and begin an investigation into the location of zeros of certain families of rational period functions.
References:
- [Ap]
- T. M. Apostol, Modular Functions and Dirichlet Series in Number, 1990, Springer-Verlag, New York. MR 90j:11001
- [Bu]
- D. A. Buell, Binary Quadratic Forms, 1989, Springer-Verlag, New York. MR 92b:11021
- [Ch]
- Y. Choie, Rational period functions for the modular group and real quadratic fields, Ill. J. Math. 33 (1989), 495-530. MR 90i:11054
- [CP1]
- Y. Choie and L. A. Parson, Rational period functions and indefinite binary quadratic forms, I, Math. Ann. 286 (1990), 697-707. MR 91d:11054
- [CP2]
- Y. Choie and L. A. Parson, Rational period functions and indefinite binary quadratic forms, II, Ill, J. Math. 35 (1991), 374-400. MR 92e:11047
- [CZ]
- Y. Choie and D. Zagier, Rational period functions for
 , A Tribute to Emil Grosswald: Number Theory and Related Analysis, Contemporary Mathematics Series, Amer. Math. Soc., pp. 89-108. MR 94g:11033 - [Ha]
- J. Hawkins, On rational period functions for the modular group, handwritten manuscript.
- [Kn1]
- M. I. Knopp, Rational period functions of the modular group, Duke Math. J. 45 (1978), 47-62. MR 58:5522
- [Kn2]
- M. I. Knopp, , II, Glasgow Math. J. 23 (1982), 185-197. MR 83g:1001
- [Kn3]
- M. I. Knopp, Recent developments in the theory of rational period functions, in Number Theory (New York, 1985/1988), Springer Lecture Notes in Math., 1383, 1989, 111-122. MR 91g:11051
- [Kn4]
- M. I. Knopp, Some new results on the Eichler cohomology of automorphic forms, Bull. Amer. Math. Soc. 80 (1974), 607-632. MR 49:9193
- [Pa]
- L. A. Parson, Rational period functions and indefinite binary quadratic forms, III, A tribute to Emil Grosswald: number theory and related analysis, 109-116, Contemp. Math., 143, Amer. Math. Soc., Providence, RI, 1993. MR 94f:11046
- [PR]
- L. A. Parson and K. Rosen, Automorphic integrals and rational period functions for the Hecke groups, Ill. J. Math. 28 (1984), 383-396. MR 85j:11049
- [Za]
- D. B. Zagier, Zetafunktionen und Quadratische Korper, 1981, Springer-Verlag, Heidelberg. MR 82m:10002
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
11F99
Retrieve articles in all Journals with
MSC (1991):
11F99
Additional Information:
Ellen
Gethner
Affiliation:
Department of Mathematics, Claremont McKenna College, Claremont, California 91711
Email:
egethner@mckenna.edu
DOI:
10.1090/S0002-9939-99-05006-6
PII:
S 0002-9939(99)05006-6
Received by editor(s):
August 10, 1996
Additional Notes:
The author's research at MSRI was supported in part by NSF grant DMS-9022140
Communicated by:
Dennis A. Hejhal
Copyright of article:
Copyright
1999,
American Mathematical Society
|
