Journal article
Correlation of zeros of automorphic L-functions
Science in China Series A: Mathematics, Vol.51(7), pp.1147-1166
07/2008
DOI: 10.1007/s11425-008-0085-0
Abstract
We compute the n-level correlation of normalized nontrivial zeros of a product of Lfunctions: L(s, π1) … L(s, π k ), where πj, j = 1, …, k, are automorphic cuspidal representations of GL mj (ℚA). Here the sizes of the groups GL mj (ℚA) are not necessarily the same. When these L(s, π j ) are distinct, we prove that their nontrivial zeros are uncorrelated, as predicted by random matrix theory and verified numerically. When L(s, π j ) are not necessarily distinct, our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble (GUE) models of individual L-functions and products of lower rank GUEs. The results are unconditional when m 1, …, m k ⩽ 4, but are under Hypothesis H in other cases.
Details
- Title: Subtitle
- Correlation of zeros of automorphic L-functions
- Creators
- Liu JianYa - School of Mathematics Shandong University Jinan 250100 ChinaYangBo Ye - Department of Mathematics The University of Iowa Iowa City IA 52242-1419 USA
- Resource Type
- Journal article
- Publication Details
- Science in China Series A: Mathematics, Vol.51(7), pp.1147-1166
- DOI
- 10.1007/s11425-008-0085-0
- ISSN
- 1006-9283
- eISSN
- 1862-2763
- Publisher
- SP Science in China Press; Heidelberg
- Language
- English
- Date published
- 07/2008
- Academic Unit
- Mathematics
- Record Identifier
- 9983985980702771
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