Journal article
Dirichlet series, asymptotics, and statistics based on functoriality from GL(2)
Research in number theory, Vol.6(4), 37
09/16/2020
DOI: 10.1007/s40993-020-00212-2
Abstract
Let πi, i=1,2,3, be unitary automorphic cuspidal representations of GL2(QA) with Fourier coefficients λπi(n). Consider an automorphic representation Π which is equivalent to ∧2(Sym3π1), π1⊠π2, π1⊠Sym2π2, ∧2(π1⊠π2), or π1×π2×π3. Since the Dirichlet series of L(s,Π×Π˜) is known to be complicated, a simpler Dirichlet series ∑λ(n)n−s is defined and analytically continued in each case, which is closely related to L(s,Π×Π˜) and catches the essence of the underlying functoriality. Asymptotics of ∑n≤xλ(n) are proved. As applications, certain means, variance, and covariances of |λπi(n)|k for k=2,4,6 and |λπi(nj)|2 for j=2,3,4 are computed. These statistics provide a deep insight of the distribution of the GL(2) Fourier coefficients λπi(n).
Details
- Title: Subtitle
- Dirichlet series, asymptotics, and statistics based on functoriality from GL(2)
- Creators
- Huixue Lao - Shandong Normal UniversityYangbo Ye - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Research in number theory, Vol.6(4), 37
- Publisher
- Springer International Publishing
- DOI
- 10.1007/s40993-020-00212-2
- ISSN
- 2522-0160
- eISSN
- 2363-9555
- Grant note
- ZR2018MA003 / Natural Science Foundation of Shandong Province
- Language
- English
- Date published
- 09/16/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984241043202771
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