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

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717712-0

MathSciNet review:
717712

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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.

**[1]**I. Kra,*Automorphic Forms and Kleinian Groups*, Benjamin, Reading, Mass., 1972. MR**0357775 (50:10242)****[2]**D. H. Lehmer, "Ramanujan's function ,"*Duke Math J.*, v. 10, 1943, pp. 483-492. MR**0008619 (5:35b)****[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]**R. Rankin,*Modular Forms and Functions*, Cambridge Univ. Press, Cambridge, 1977. MR**0498390 (58:16518)**

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0717712-0

Article copyright:
© Copyright 1983
American Mathematical Society