Journal article
Perron's formula and the prime number theorem for automorphic L-functions
Pure and applied mathematics quarterly, Vol.3(2), pp.481-497
2007
DOI: 10.4310/PAMQ.2007.v3.n2.a4
Abstract
In this paper the classical Perron’s formula is modified so that it now depends no longer on sizes of individual terms but on a sum over a short interval. When applied to automorphic L-functions, this new Perron’s formula may allow one to avoid estimation of individual Fourier coefficients, without assuming the Generalized Ramanujan Conjecture (GRC). As an application, a prime number theorem for Rankin-Selberg L-functions L(s, π × π̃′) is proved unconditionally without assuming GRC, where π and π′ are automorphic irreducible cuspidal representations of GLm(QA) and GLm′(QA), respectively. 2000 Mathematics Subject Classification: 11F70, 11M26, 11M41.
Details
- Title: Subtitle
- Perron's formula and the prime number theorem for automorphic L-functions
- Creators
- Jianya LiuYangbo Ye
- Resource Type
- Journal article
- Publication Details
- Pure and applied mathematics quarterly, Vol.3(2), pp.481-497
- DOI
- 10.4310/PAMQ.2007.v3.n2.a4
- ISSN
- 1558-8599
- eISSN
- 1558-8602
- Language
- English
- Date published
- 2007
- Academic Unit
- Mathematics
- Record Identifier
- 9983985934502771
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