TY - JOUR

T1 - The adjoint representation L-function for GL(n)

AU - Flicker, Yuval Z.

PY - 1992/6

Y1 - 1992/6

N2 - Ideas underlying the proof of the "simple" trace formula are used to show the following. Let F be a global field, and A its ring of adeles. Let π be a cuspidal representation of GL(n, A) which has a supercuspidal component, and ω a unitary character of Ax/Fx. Let S0 be a complex number such that for every separable extension E of F of degree n, the L-function L(s, ω o NormE/F) over E vanishes at s = s0 to the order m ≥ 0.; Then the product L-function L(s, π ⊗ ω × π) vanishes at s = So to the order m. This result is a reflection of the fact that the tensor product of a finite dimensional representation with its contragredient contains a copy of the trivial representation.

AB - Ideas underlying the proof of the "simple" trace formula are used to show the following. Let F be a global field, and A its ring of adeles. Let π be a cuspidal representation of GL(n, A) which has a supercuspidal component, and ω a unitary character of Ax/Fx. Let S0 be a complex number such that for every separable extension E of F of degree n, the L-function L(s, ω o NormE/F) over E vanishes at s = s0 to the order m ≥ 0.; Then the product L-function L(s, π ⊗ ω × π) vanishes at s = So to the order m. This result is a reflection of the fact that the tensor product of a finite dimensional representation with its contragredient contains a copy of the trivial representation.

UR - http://www.scopus.com/inward/record.url?scp=84974005051&partnerID=8YFLogxK

U2 - 10.2140/pjm.1992.154.231

DO - 10.2140/pjm.1992.154.231

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AN - SCOPUS:84974005051

SN - 0030-8730

VL - 154

SP - 231

EP - 244

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -