Transfer from GSO(4) to GL(4) and L-functions

Bogume Jang, Purdue University

Abstract

We show the existence of an L-functions of a cuspidal representation of GSp(4, [special characters omitted]) × GSp(4, [special characters omitted]) which has a pole of order 2 at s = 1, even for globally generic representations. However if π comes from GSO(4, [special characters omitted]), then π is the Weil transfer of Π1 ⊗ Π 2 realized as a representation of GSO(4, [special characters omitted]). This agrees with Langlands Functoriality principle as GSO(4) is an endoscopic group for GSp(4) and shows that data Π1 ⊗ Π 2 on GSO(4) transfers to Π1 [special characters omitted] Π2 through the composite of the endoscopic transfer from GSO(4) to GSp(4) and the twisted endoscopic transfer from GSp(4) to GL(4). Moreover, when ρ2, ρ3 denote the standard representations of GL(2, [special characters omitted]), GL(3, [special characters omitted]) and π2, π3 are two cuspidal representations of GL(2, [special characters omitted]), GL(3, [special characters omitted]), we show that the L-functions LS( s, π2 ⊗ π3, ρ 2 ⊗ Adρ3) extends to a meromorphic function of s on all of [special characters omitted] and satisfies a standard functional equation.

Degree

Ph.D.

Advisors

Shahidi, Purdue University.

Subject Area

Mathematics

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