# 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…

## 2 Citations

Deligne's conjecture for automorphic motives over CM-fields, Part I: factorization

- Mathematics
- 2018

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

- MathematicsInternational 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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