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Mathematics of Computation
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
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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?)

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  • [2] D. H. Lehmer, Ramanujan’s function 𝜏(𝑛), Duke Math. J. 10 (1943), 483–492. MR 0008619 (5,35b)
  • [3] J. C. Nash, "Function minimizations," Interface Age, v. 7, 1982, pp. 34-42.
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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1983-0717712-0
PII: S 0025-5718(1983)0717712-0
Article copyright: © Copyright 1983 American Mathematical Society