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arXiv · 1312.5955

Critical values of Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions for GL(2)

A. Raghuram
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Abstract

In a previous article we had proved an algebraicity result for the central critical value for L-functions for GL(n) x GL(n-1) over Q assuming the validity of a nonvanishing hypothesis involving archimedean integrals. The purpose of this article is to generalize that result for all critical values for L-functions for GL(n) x GL(n-1) over any number field F. Binyong Sun has recently proved that nonvanishing hypothesis and so the results of this article are unconditional. Using such results for the case of GL(3) x GL(2), new unconditional algebraicity results for the special values of symmetric cube L-functions for GL(2) over F have been proved.

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A. Raghuram. 2015-03-04. Critical values of Rankin-Selberg L-functions for GL(n) x GL(n-1) and the symmetric cube L-functions for GL(2). https://arxiv.org/abs/1312.5955

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