Relations of rationality for special values of Rankin–Selberg L-functions of GLn×GLm over CM-fields

@article{Grobner2020RelationsOR,
  title={Relations of rationality for special values of
Rankin–Selberg L-functions of GLn×GLm over CM-fields},
  author={Harald Grobner and Gunja Sachdeva},
  journal={Pacific Journal of Mathematics},
  year={2020},
  volume={308},
  pages={281-305}
}
In this paper we present a bridge between automorphic forms of general reductive groups and motives over number elds, hinting a translation of Deligne's conjecture for motivic L-functions into a precise automorphic context. The bulk of this article provides evidence for such an automorphic translation by considering the case of Rankin Selberg L-functions L(s,Π× Π′) of GLn × GLm over CMelds F . Our main results are of two di erent kinds: Firstly, for arbitrary integers 1 ≤ m ≤ n, and suitable… 
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2 Citations

2 Citations

Deligne's conjecture for automorphic motives over CM-fields, Part I: factorization
This is the first of two papers devoted to the relations between Deligne's conjecture on critical values of motivic $L$-functions and the multiplicative relations between periods of arithmetically…
Special Values of L-functions for GL(n) Over a CM Field
  • A. Raghuram
  • Mathematics
    International Mathematics Research Notices
  • 2021
We prove a Galois-equivariant algebraicity result for the ratios of successive critical values of $L$-functions for ${\textrm GL}(n)/F,$ where $F$ is a totally imaginary quadratic extension of a…

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