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RANKIN–SELBERG INTEGRALS FOR LOCAL SYMMETRIC SQUARE FACTORS ON G L ( 2 )
Author(s) -
Jo Yeongseong
Publication year - 2021
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12079
Subject(s) - mathematics , square (algebra) , local field , pure mathematics , zero (linguistics) , residual , function (biology) , combinatorics , geometry , philosophy , linguistics , algorithm , evolutionary biology , biology
Let π be an irreducible admissible (complex) representation of G L ( 2 ) over a non‐Archimedean characteristic zero local field with odd residual characteristic. In this paper, we prove the equality between the local symmetric square L ‐function associated to π arising from integral representations and the corresponding Artin L ‐function for its Langlands parameter through the local Langlands correspondence. With this in hand, we show the stability of local symmetric γ‐factors attached to π under highly ramified twists.