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• W2004348490 abstract "Let π and π′ be unitary automorphic cuspidal representations of GLm(QA) and GLm′(QA), respectively, where at least one of π and π′ is self-contragredient. Using the prime number theorem for Rankin–Selberg L-functions, we compute a sharper version of Selberg orthogonality that contains certain lower-order terms which depend on special values of the Rankin–Selberg L-function attached to the pair (π,π′) and a sum related to Hypothesis H. In a case by case analysis when m,m′⩽4 and Hypothesis H is known to be true, we show how the constants involved in the lower-order terms can be expressed in terms of special values of Rankin–Selberg convolutions of symmetric- and/or exterior-power L-functions. In addition to showing that these constants give arithmetic information about the representations π and π′, we demonstrate how Hypothesis H can be used to give analytic continuation of the L-functions involved in the computation of the constants." @default.
• W2004348490 created "2016-06-24" @default.
• W2004348490 creator A5017183872 @default.
• W2004348490 creator A5048538009 @default.
• W2004348490 date "2014-08-01" @default.
• W2004348490 modified "2023-09-26" @default.
• W2004348490 title "The prime number theorem and Hypothesis H with lower-order terms" @default.
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• W2004348490 doi "https://doi.org/10.1016/j.jnt.2014.01.022" @default.
• W2004348490 hasPublicationYear "2014" @default.
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