On the dimension of the space of theta functions
HTML articles powered by AMS MathViewer
- by Daniel Bump and Alexander Pekker
- Proc. Amer. Math. Soc. 130 (2002), 3473-3481
- DOI: https://doi.org/10.1090/S0002-9939-02-06570-X
- Published electronically: April 22, 2002
- PDF | Request permission
Abstract:
We compute the dimension of the space of theta functions of a given type using a variant of the Selberg trace formula.References
- V. Bargman, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961) 187–214.
- Pierre Cartier, Quantum mechanical commutation relations and theta functions, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 361–383. MR 0216825
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
- G. Frobenius, Über die Grundlagen der Theorie der Jacobischen Functionen, J. Reine Angew. Math. 97 (1884), 188–223.
- Dennis A. Hejhal, Kernel functions, Poincaré series, and LVA, In the tradition of Ahlfors and Bers (Stony Brook, NY, 1998) Contemp. Math., vol. 256, Amer. Math. Soc., Providence, RI, 2000, pp. 173–201. MR 1759678, DOI 10.1090/conm/256/04005
- Norman E. Hurt, Geometric quantization in action, Mathematics and its Applications (East European Series), vol. 8, D. Reidel Publishing Co., Dordrecht-Boston, Mass., 1983. MR 689710
- Jun-ichi Igusa, Theta functions, Die Grundlehren der mathematischen Wissenschaften, Band 194, Springer-Verlag, New York-Heidelberg, 1972. MR 0325625
- Serge Lang, Introduction to algebraic and abelian functions, 2nd ed., Graduate Texts in Mathematics, vol. 89, Springer-Verlag, New York-Berlin, 1982. MR 681120
- D. J. Newman and H. S. Shapiro, Certain Hilbert spaces of entire functions, Bull. Amer. Math. Soc. 72 (1966), 971–977. MR 205055, DOI 10.1090/S0002-9904-1966-11608-7
- V. Kumar Murty, Introduction to abelian varieties, CRM Monograph Series, vol. 3, American Mathematical Society, Providence, RI, 1993. MR 1231797, DOI 10.1090/crmm/003
- Ichiro Satake, Fock representations and theta-functions, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) Ann. of Math. Studies, No. 66, Princeton Univ. Press, Princeton, N.J., 1971, pp. 393–405. MR 0424698
- Atle Selberg, Collected papers. Vol. I, Springer-Verlag, Berlin, 1989. With a foreword by K. Chandrasekharan. MR 1117906
- Hideo Shimizu, On discontinuous groups operating on the product of the upper half planes, Ann. of Math. (2) 77 (1963), 33–71. MR 145106, DOI 10.2307/1970201
- H. P. F. Swinnerton-Dyer, Analytic theory of abelian varieties, London Mathematical Society Lecture Note Series, No. 14, Cambridge University Press, London-New York, 1974. MR 0366934
- André Weil, Sur certains groupes d’opérateurs unitaires, Acta Math. 111 (1964), 143–211 (French). MR 165033, DOI 10.1007/BF02391012
Bibliographic Information
- Daniel Bump
- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
- Email: bump@math.stanford.edu
- Alexander Pekker
- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
- Address at time of publication: 1841 Palisades Drive, Santa Rosa, California 95403
- Email: apekker@stanfordalumni.org
- Received by editor(s): July 12, 2001
- Published electronically: April 22, 2002
- Additional Notes: We would like to thank Dennis Hejhal for help with the references.
- Communicated by: Dennis A. Hejhal
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3473-3481
- MSC (2000): Primary 14K25
- DOI: https://doi.org/10.1090/S0002-9939-02-06570-X
- MathSciNet review: 1918823