2015/03/27 by Aaron Pollack, Pollack, Aaron, Shrenik Shah +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.1503.08197
We give two global integrals that unfold to a non-unique model and represent the partial Spin L-function on GSp6. We deduce that for a wide class of cuspidal automorphic representations π, the partial Spin L-function is holomorphic except for a possible simple pole at s=1, and that the presence of such a pole indicates that π is an exceptional theta lift from G2. These results utilize and extend previous work of Gan and Gurevich, who introduced one of the global integrals and proved these facts for a special subclass of these π upon which the aforementioned model becomes unique. The other integral can be regarded as a higher rank analogue of the integral of Kohnen-Skoruppa on GSp4.