The second moment of $GL(3) \times GL(2)$ $L$-functions, integrated

Details The second moment of $GL(3) \times GL(2)$ $L$-functions, integrated The second moment of $GL(3) \times GL(2)$ $L$-functions, integrated

2009-03-09

arxiv.org/abs/0903.1575v2

Adv. Math. 226 (2011), no. 4, 3550-3578

Mathematics

Number Theory

v1: 17 pages; v2: 24 pages, improved and expanded exposition

Scientific paper

10.1016/j.aim.2010.10.021

We consider the family of Rankin-Selberg convolution L-functions of a fixed
SL(3, Z) Maass form with the family of Hecke-Maass cusp forms on SL(2, Z). We
estimate the second moment of this family of L-functions with a "long"
integration in t-aspect. These L-functions are distinguished by their high
degree (12) and large conductors (of size T^{12}).

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