L-factor of irreducible χ₁ × χ₂ ⋊ σ

Abstract

The L-factor of irreducible χ₁ × χ₂ ⋊ σ defined by Piatetski-Shapiro is computed by using non-split Bessel functional.

Keywords

Bessel model / L-factor / GSp(4) / Regular pole

References

[1] Bump D.. Automorphic Forms and Representations, 1998, New York, NY, USA: Cambridge Studies in Advanced Mathematics

[2] Casselman, W., Introductions to the theory of admissible representations of reductive p-adic groups, preprint.

[3] Danisman Y.. Regular poles for the p-adic group GSp₄. Turk. J. Math., 2014, 38: 587-613

[4] Danisman Y.. Regular poles for the p-adic group GSp₄-II. Turk. J. Math., 2015, 39: 369-394

[5] Danisman Y.. Local factors of nongeneric supercuspidal representations of GSp₄. Math. Ann., 2015, 361: 1073-1121

[6] Gan W., Takeda S.. The local Langlands conjecture for GSp(4). Ann. Math., 2011, 173: 1841-1882

[7] Piatetski-Shapiro I.. L-functions for GSp₄. Pacific J. Math., 1997 259-275

[8] Prasad D., Takloo-Bighash R.. Bessel models for GSp(4). J. Reine und Angew Math. (Crelles J.), 2011, 655: 189-243

[9] Roberts B., Schmidt R.. New Forms for GSp(4), Springer Lecture Notes in Mathematics, 2007, Heidelberg, Germany: Springer-Verlag

[10] Roberts B., Schmidt R.. Some remarks on Bessel functionals for GSp(4). Documenta Math., 2016, 21: 467-553

[11] Shahidi F.. A proof of Langlands conjecture on plancherel measures; complementary series for p-adic groups. Ann. Math., 1990, 132: 273-330

[12] Takloo-Bighash R.. L-functions for the p-adic group GSp(4). Amer. J. Math., 2000, 122: 1085-1120

[13] Tunnell J.. Local L-factors and characters of GL(2). Amer. J. Math., 1983, 105: 1277-1307