Towards Functoriality Of Spinor L-functions

Details Towards Functoriality Of Spinor L-functions Towards Functoriality Of Spinor L-functions

2008-08-25

arxiv.org/abs/0808.3389v1

Mathematics

Number Theory

19 pages

Scientific paper

The object of this work is the spinor L-function of degree 3 and certain degeneration related to the functoriality principle. We study liftings of automorphic forms on the pair of symplectic groups $(\text{GSp}(2),\text{GSp}(4))$ to $\text{GSp}(6)$. We prove cuspidality and demonstrate the compatibility with conjectures of Andrianov, Panchishkin, Deligne and Yoshida. This is done on a motivic and analytic level. We discuss an underlying torus and L-group homomorphism and put our results in the context of the Langlands program.

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