A Specialisation of the Bump-Friedberg L-function

作者：Matringe Nadir^*

来源：Canadian Mathematical Bulletin, 2015, 58(3): 580-595.

DOI：10.4153/CMB-2015-014-1

• automorphic L functions

We study the restriction of Bump-Friedberg integrals to affine lines {(s + alpha, 2s), s is an element of C}. It has simple theory, very close to that of the Asai L-function. It is an integral representation of the product L(s + alpha,pi)L(2s, Lambda(2), pi), which we denote by L-lin (s, pi, alpha) for this abstract, when pi is a cuspidal automorphic representation of GL(k, A) for A the adeles of a number field. When k is even, we show that the partial L-function L-lin,L-S (s, pi, alpha) has a pole at 1/2 if and only if pi admits a (twisted) global period. This gives a more direct proof of a theorem of Jacquet and Friedberg, asserting that pi has a twisted global period if and only if L (alpha + 1/2, pi) not equal 0 and L(1, Lambda(2), pi) = infinity. When k is odd, the partial L-function is holmorphic in a neighbourhood of Re(s) >= 1/2 when Re(alpha) is >= 0.

• 出版日期2015-9