Open Access
May 2004 Estimates of automorphic $L$-functions in the discriminant-aspect
Chiharu Kaminishi
Proc. Japan Acad. Ser. A Math. Sci. 80(5): 42-46 (May 2004). DOI: 10.3792/pjaa.80.42


Let $L(s,\phi)$ be an automorphic $L$-function for a Bianchi group defined via an imaginary quadratic field with discriminant $d < 0$. We give an upper bound for the absolute value of $L(s, \phi)$ in terms of $\Im(s)$, the Laplace eigenvalue and the discriminant $d$. The bound as $d \to \infty$ presents a new aspect in the study of $L$-functions.


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Chiharu Kaminishi. "Estimates of automorphic $L$-functions in the discriminant-aspect." Proc. Japan Acad. Ser. A Math. Sci. 80 (5) 42 - 46, May 2004.


Published: May 2004
First available in Project Euclid: 18 May 2005

zbMATH: 1065.11030
MathSciNet: MR2062798
Digital Object Identifier: 10.3792/pjaa.80.42

Primary: 11F66
Secondary: 32A40

Keywords: automorphic form , convexity bound , Maass form

Rights: Copyright © 2004 The Japan Academy

Vol.80 • No. 5 • May 2004
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