Rankin–Selberg gamma factors of level zero representations of GLn
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Rongqing Ye
Abstract
For a p-adic local field F of characteristic 0, with residue field
Acknowledgements
The author thanks his advisor, Prof. James Cogdell, for helpful comments and discussions. We thank Qing Zhang for pointing out references on local converse theorem over finite fields. We appreciate the referee’s comments and suggestions, which help make the paper more readable.
References
[1]
M. Adrian, B. Liu, S. Stevens and P. Xu,
On the Jacquet conjecture on the local converse problem for p-adic
[2]
C. J. Bushnell, G. M. Henniart and P. C. Kutzko,
Local Rankin-Selberg convolutions for
[3]
C. J. Bushnell and P. C. Kutzko,
The Admissible Dual of
[4] J. Chai, Bessel functions and local converse conjecture of Jacquet, J. Eur. Math. Soc. (JEMS), to appear. 10.4171/JEMS/870Search in Google Scholar
[5] S. I. Gel’fand, Representations of the full linear group over a finite field, Math. USSR Sb. 12 (1970), no. 13, 13–39. 10.1070/SM1970v012n01ABEH000907Search in Google Scholar
[6] I. M. Isaacs, Character Theory Of Finite Groups, AMS Chelsea, Providence, 2006. 10.1090/chel/359Search in Google Scholar
[7]
H. Jacquet and B. Liu,
On the local converse theorem for p-adic
[8] H. Jacquet, I. I. Piatetskii-Shapiro and J. Shalika, Rankin–Selberg convolutions, Amer. J. Math. 105 (1983), no. 2, 367–464. 10.2307/2374264Search in Google Scholar
[9]
D. Jiang, C. Nien and S. Stevens,
Towards the Jacquet conjecture on the local converse problem for p-adic
[10] J.-L. Kim, An inductive formula for ϵ-factors, Automorphic Forms and Related Geometry: Assessing the Legacy of I. I. Piatetski-Shapiro, Contemp. Math. 614, American Mathematical Society, Providence (2014), 243–260. 10.1090/conm/614/12266Search in Google Scholar
[11] C. Nien, A proof of the finite field analogue of Jacquet’s conjecture, Amer. J. Math. 136 (2014), no. 3, 653–674. 10.1353/ajm.2014.0020Search in Google Scholar
[12] C. Nien and L. Zhang, Converse theorem meets Gauss sums (with an appendix by Zhiwei Yun, preprint (2018), https://arxiv.org/abs/1806.04850. Search in Google Scholar
[13] V. Paskunas and S. Stevens, On the realization of maximal simple types and epsilon factors of pairs, Amer. J. Math. 130 (2008), no. 5, 1211–1261. 10.1353/ajm.0.0022Search in Google Scholar
[14] I. I. Piatetski-Shapiro, Lecture note 1976. Search in Google Scholar
[15] E.-A. Roditty, On gamma factors and bessel functions for representations of general linear groups over finite fields, Master’s thesis, Tel Aviv University, 2010. Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups
- Infinite families of equivariantly formal toric orbifolds
- Bounds for GL3L-functions in depth aspect
- Nonlinear Dirichlet problems with unilateral growth on the reaction
- K-invariant cusp forms for reductive symmetric spaces of split rank one
- Cellularity in quotient spaces of topological groups
- Shifted convolution sums for higher rank groups
- Dimension quotients, Fox subgroups and limits of functors
- Large sums of Hecke eigenvalues of holomorphic cusp forms
- K-theory classification of graded ultramatricial algebras with involution
- Regularity of symbolic powers and arboricity of matroids
- On some problems concerning symmetrization operators
- An Erdős–Ko–Rado result for sets of pairwise non-opposite lines in finite classical polar spaces
- Rankin–Selberg gamma factors of level zero representations of GLn
- Sobolev’s inequality for double phase functionals with variable exponents
- Independence of Artin L-functions
- Oscillatory singular integral operators with Hölder class kernels on Hardy spaces
Articles in the same Issue
- Frontmatter
- Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups
- Infinite families of equivariantly formal toric orbifolds
- Bounds for GL3L-functions in depth aspect
- Nonlinear Dirichlet problems with unilateral growth on the reaction
- K-invariant cusp forms for reductive symmetric spaces of split rank one
- Cellularity in quotient spaces of topological groups
- Shifted convolution sums for higher rank groups
- Dimension quotients, Fox subgroups and limits of functors
- Large sums of Hecke eigenvalues of holomorphic cusp forms
- K-theory classification of graded ultramatricial algebras with involution
- Regularity of symbolic powers and arboricity of matroids
- On some problems concerning symmetrization operators
- An Erdős–Ko–Rado result for sets of pairwise non-opposite lines in finite classical polar spaces
- Rankin–Selberg gamma factors of level zero representations of GLn
- Sobolev’s inequality for double phase functionals with variable exponents
- Independence of Artin L-functions
- Oscillatory singular integral operators with Hölder class kernels on Hardy spaces
