Periods and (χ, b)-factors of cuspidal automorphic forms of symplectic groups
- 38 Downloads
In this paper, we introduce a new family of period integrals attached to irreducible cuspidal automorphic representations σ of symplectic groups Sp2n(A), which detects the right-most pole of the L-function L(s, σ × χ) for some character χ of F×A × of order at most 2, and hence the occurrence of a simple global Arthur parameter (χ, b) in the global Arthur parameter ψ attached to σ. We also give a characterisation of first occurrences of theta correspondence by (regularised) period integrals of residues of certain Eisenstein series.
Unable to display preview. Download preview PDF.
- [Art13]J. Arthur, The Endoscopic Classification of Representations, American Mathematical Society Colloquium Publications, Vol. 61, American Mathematical Society, Providence, RI, 2013.Google Scholar
- [GJRS11]D. Ginzburg, D. Jiang, S. Rallis D. Soudry, L-functions for symplectic groups using Fourier–Jacobi models, in Arithmetic Geometry and Automorphic Forms, Advanced Lectures in Mathematics, Vol. 19, International Press, Somerville, MA, 2011, pp. 183–207.Google Scholar
- [GPSR87]S. Gelbart, I. Piatetski-Shapiro and S. Rallis, Explicit Constructions of Automorphic L-functions, Lecture Notes in Mathematics, Vol. 1254, Springer-Verlag, Berlin, 1987.Google Scholar
- [Jia14]D. Jiang, Automorphic integral transforms for classical groups I: Endoscopy correspondences, in Automorphic Forms and Related Geometry: Assessing the Legacy of I. I. Piatetski-Shapiro, Contemporary Mathematics, Vol. 614, American Mathematical Society, Providence, RI, 2014, pp. 179–242.CrossRefGoogle Scholar
- [JW14]D. Jiang and C. Wu, On (χ, b)-factors of cuspidal automorphic representations of unitary groups. II, preprint, 2014.Google Scholar
- [KR90]S. S. Kudla and S. Rallis, Poles of Eisenstein series and L-functions, in Festschrift in Honor of I. I. Piatetski-Shapiro on the Occasion of his Sixtieth Birthday, Part II (Ramat Aviv, 1989), Israel Mathematical Conference Proceedings, Vol. 3, Weizmann, Jerusalem, 1990, pp. 81–110.MathSciNetzbMATHGoogle Scholar
- [Lan71]R. P. Langlands, Euler Products, Yale Mathematical Monographs, Vol. 1, Yale University Press, New Haven, Conn.-London, 1971.Google Scholar
- [MW95]C. Moeglin and J.-L. Waldspurger, Spectral Decomposition and Eisenstein Series, Cambridge Tracts in Mathematics, Vol. 113, Cambridge University Press, Cambridge, 1995.Google Scholar
- [Sha10]F. Shahidi, Eisenstein Series and Automorphic L-functions, American Mathematical Society Colloquium Publications, Vol. 58, American Mathematical Society, Providence, RI, 2010.Google Scholar
- [She13]X. Shen, Unramified computation of tensor L-functions on symplectic groups, Ph.D. Thesis, University of Minnesota, ProQuest LLC, Ann Arbor, MI, 2013.Google Scholar