Quadratic base change and the analytic continuation of the Asai L-function: A new trace formula approach

@article{Herman2010QuadraticBC,
  title={Quadratic base change and the analytic continuation of the Asai L-function: A new trace formula approach},
  author={P. Edward Herman},
  journal={American Journal of Mathematics},
  year={2010},
  volume={138},
  pages={1669 - 1729}
}
  • P. E. Herman
  • Published 23 August 2010
  • Mathematics
  • American Journal of Mathematics
Abstract:Using Langlands's beyond endoscopy idea, we study the Asai $L$-function associated to a real quadratic field $\Bbb{K}/\Bbb{Q}$. We prove that the Asai $L$-function associated to a cuspidal automorphic representation over $\Bbb{K}$ has analytic continuation to the complex plane with at most a simple pole at $s=1$. We then show if the $L$-function has a pole then the representation is a base change from $\Bbb{Q}$. While this result is known using integral representations from the work of… 
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