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Zeros of L-functions attached to Maass forms

Epstein, Charles and Hafner, James Lee and Sarnak, Peter (1985) Zeros of L-functions attached to Maass forms. Mathematische Zeitschrift, 190 (1). pp. 113-128. ISSN 0025-5874. doi:10.1007/BF01159169.

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This paper considers PSL(2,ℤ)-automorphic cusp forms (the Maass forms) and their associated Dirichlet series. There are two major results. The first uses real variable techniques to give an explicit reconstruction of the cusp form in terms of the Dirichlet series. This representation is valid in the entire upper half-plane. The second uses this representation to show that the Dirichlet series has many zeros on its critical line. This is the analogue of the Hardy-Littlewood result for the Riemann zeta function.

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Additional Information:© 1985 Springer-Verlag. Received April 16, 1984.
Issue or Number:1
Record Number:CaltechAUTHORS:20131015-144745068
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41925
Deposited By: Tony Diaz
Deposited On:16 Oct 2013 19:41
Last Modified:10 Nov 2021 04:35

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