2013
DOI: 10.1142/s1793042113500310
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Factorization of Automorphic L-Functions and Their Zero Statistics

Abstract: In this paper we define a Rankin–Selberg L-function attached to two Galois invariant automorphic cuspidal representations of GL m(𝔸E) and GL m′(𝔸F) over cyclic Galois extensions E and F of prime degree. This differs from the classical case in that the two extension fields E and F could be completely unrelated to one another, and we exploit the existence of the automorphic induction functor over cyclic extensions (see [J. Arthur and L. Clozel, Simple Algebras, Base Change, and the Advanced Theory of the Trace… Show more

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Cited by 2 publications
(1 citation statement)
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“…A prime number theorem was derived in the case where and are cyclic of prime degree in [15]. Using this, the author computed the correlation function of a product ( , 1 ) ( , 2 ) ⋅ ⋅ ⋅ ( , ) in [16] assuming is cyclic of prime degree for = 1, 2, . .…”
Section: Introductionmentioning
confidence: 99%
“…A prime number theorem was derived in the case where and are cyclic of prime degree in [15]. Using this, the author computed the correlation function of a product ( , 1 ) ( , 2 ) ⋅ ⋅ ⋅ ( , ) in [16] assuming is cyclic of prime degree for = 1, 2, . .…”
Section: Introductionmentioning
confidence: 99%