Automorphic SL₂-periods and the subconvexity problem for GL₂ × GL₃

2020/01/09 by Pal, Aprameyo, de Vera-Piquero, Carlos
#11F27 #11F37 #11F67 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2001.03186

Abstract

We prove a new (conditional) result towards the subconvexity problem for certain automorphic L-functions for GL₂ × GL₃. This follows from the computation of new SL₂-period integrals associated with newforms f and g of even weight and odd squarefree level. The same computations also lead to a central value formula for degree 6 complex L-series of the form L(f ⊗ Ad(g), s), extending previous work in arXiv:1804.02352.

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