Journal article
The prime number theorem and Hypothesis H with lower-order terms
Journal of number theory, Vol.141, pp.59-82
08/2014
DOI: 10.1016/j.jnt.2014.01.022
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.
Details
- Title: Subtitle
- The prime number theorem and Hypothesis H with lower-order terms
- Creators
- Timothy L Gillespie - Department of Mathematics, St. Ambrose University, Davenport, IA, United StatesYangbo Ye - Department of Mathematics, The University of Iowa, Iowa, IA, United States
- Resource Type
- Journal article
- Publication Details
- Journal of number theory, Vol.141, pp.59-82
- DOI
- 10.1016/j.jnt.2014.01.022
- ISSN
- 0022-314X
- eISSN
- 1096-1658
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 08/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9983985861102771
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