2009
DOI: 10.1017/s1474748009000188
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Subconvexity bounds for automorphicL-functions

Abstract: We break the convexity bound in thet-aspect forL-functions attached to cusp formsffor GL2(k) over arbitrary number fieldsk. The argument uses asymptotics with error term with a power saving, for second integral moments over spectral families of twistsL(s,f⊗χ) by Grossencharacters χ, from our previous paper on integral moments.

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Cited by 15 publications
(20 citation statements)
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References 43 publications
(54 reference statements)
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“…Over general number fields the conductor aspect was obtained by the second author [65] and Diaconu-Garrett for the t-aspect [16]. The various methods used in these papers, although superficially rather different and having different strengths and weaknesses, nonetheless are closely linked; they are all, in various ways, related to versions of the identity described in Section 4.5.3.…”
Section: Subconvexity Of Character Twistsmentioning
confidence: 99%
“…Over general number fields the conductor aspect was obtained by the second author [65] and Diaconu-Garrett for the t-aspect [16]. The various methods used in these papers, although superficially rather different and having different strengths and weaknesses, nonetheless are closely linked; they are all, in various ways, related to versions of the identity described in Section 4.5.3.…”
Section: Subconvexity Of Character Twistsmentioning
confidence: 99%
“…Recently P. Michel and A. Venkatesh [17] and A. Diaconu and P. Garrett [4] proved the estimate that we need in general: Theorem 8.3. There exists some δ > 0 such that…”
Section: The Standard L-functionmentioning
confidence: 82%
“…Choose 11 18 < δ 0 < 1. For δ 0 (w ) 1 + , and by Phragmen-Lindelöf, Z (δ 0 + iη) has polynomial growth of exponent less than 1 2 (see Section 4 in [10]). Consider the rectangle R with vertices at δ 0 − i S, β − i S, β + i S, δ 0 + i S. Recall Perron's formula: for β > 1,…”
Section: Subconvexity Boundsmentioning
confidence: 99%
“…The method applies to GL 2 over an arbitrary number field. Until the recent works [9,10], which exclusively address t-aspect moments, there were no results on moments over arbitrary number fields. Here we use spectral methods to address non-archimedean conductor aspect moments.…”
mentioning
confidence: 99%
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