Contributions from conjugacy classes of regular elliptic elements in to the dimension formula

Author:
Min King Eie

Journal:
Trans. Amer. Math. Soc. **285** (1984), 403-410

MSC:
Primary 11F46; Secondary 11F72

MathSciNet review:
748846

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The dimension of the space of cusp forms on the degree Siegel upper half-space can be obtained from the Selberg trace formula; in this paper we compute the contribution from the conjugacy classes of regular elliptic elements in using Weyl's character formula for representations of .

**[1]**Hermann Boerner,*Representations of groups*, North-Holland, Amsterdam, 1970.**[2]**Minking Eie,*Dimension formulas for the vector spaces of Siegel's cusp forms of degree two and degree three*, Dissertation, University of Chicago, December 1982.**[3]**R. Godement,*Généralités sur les formes modulaires*. I, II, Séminaire Henri Cartan, 10e années, 1957, 1958.**[4]**L. K. Hua,*On the theory of functions of several complex variables*. I, II, III, Amer. Math. Soc. Transl.**32**(1962), 163-263.**[5]**-,*Inequalities involving determinants*, Amer. Math. Soc. Transl.**32**(1962), 265-272.**[6]**Hans Maass,*Siegel’s modular forms and Dirichlet series*, Lecture Notes in Mathematics, Vol. 216, Springer-Verlag, Berlin-New York, 1971. Dedicated to the last great representative of a passing epoch. Carl Ludwig Siegel on the occasion of his seventy-fifth birthday. MR**0344198****[7]**Sigurđur Helgason,*Differential geometry and symmetric spaces*, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR**0145455****[8]**George W. Machkey,*Unitary group representation in physics, probability and number theory*, Benjamin, New York, 1978.**[9]**Hideo Shimizu,*On discontinuous groups operating on the product of the upper half planes*, Ann. of Math. (2)**77**(1963), 33–71. MR**0145106**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
11F46,
11F72

Retrieve articles in all journals with MSC: 11F46, 11F72

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0748846-X

Article copyright:
© Copyright 1984
American Mathematical Society