A lower bound for the norm of the theta operator
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- by L. Alayne Parson PDF
- Math. Comp. 41 (1983), 683-685 Request permission
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
- Irwin Kra, Automorphic forms and Kleinian groups, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Reading, Mass., 1972. MR 0357775
- D. H. Lehmer, Ramanujan’s function $\tau (n)$, Duke Math. J. 10 (1943), 483–492. MR 8619 J. C. Nash, "Function minimizations," Interface Age, v. 7, 1982, pp. 34-42. R. O’Neill, "Function minimization using a simplex procedure," Applied Statistics, v. 20, 1971, pp. 338-345.
- Robert A. Rankin, Modular forms and functions, Cambridge University Press, Cambridge-New York-Melbourne, 1977. MR 0498390
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Math. Comp. 41 (1983), 683-685
- MSC: Primary 30F35; Secondary 11F11
- DOI: https://doi.org/10.1090/S0025-5718-1983-0717712-0
- MathSciNet review: 717712