Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A lower bound for the norm of the theta operator

Author: L. Alayne Parson
Journal: Math. Comp. 41 (1983), 683-685
MSC: Primary 30F35; Secondary 11F11
MathSciNet review: 717712
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Poincaré theta operator maps the space of holomorphic functions with period one onto the space of cusp forms for a finitely generated Fuchsian group. It is easy to show that the norm of the operator does not exceed one. In the case of the classical modular group and weight six, it is now shown that the norm is bounded below by .927.

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

  • [1] Irwin Kra, Automorphic forms and Kleinian groups, W. A. Benjamin, Inc., Reading, Mass., 1972. Mathematics Lecture Note Series. MR 0357775
  • [2] D. H. Lehmer, Ramanujan’s function 𝜏(𝑛), Duke Math. J. 10 (1943), 483–492. MR 0008619
  • [3] J. C. Nash, "Function minimizations," Interface Age, v. 7, 1982, pp. 34-42.
  • [4] R. O'Neill, "Function minimization using a simplex procedure," Applied Statistics, v. 20, 1971, pp. 338-345.
  • [5] Robert A. Rankin, Modular forms and functions, Cambridge University Press, Cambridge-New York-Melbourne, 1977. MR 0498390

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 30F35, 11F11

Retrieve articles in all journals with MSC: 30F35, 11F11

Additional Information

Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society