Date/Time:04 Sep 2019 10:00Venue: S16 #03-09Speaker: Cheng Yao, SinicaSpecial Value formula for twisted triple product L-function and an application to the restricted L^2-norm problemIn this talk we will present an explicit Ichino’s formula [Ich08] for the central value of the twisted triple product L-function associated to Maass forms. To establish such a formula one need to carry out explicit computations for the local period integrals appearing in Ichino’s formula. We prove an identity between the local period integral and a product of two Rankin-Selberg integrals in order to simplify the calculations. This identity generalizes the result in [MV10]. Our explicit formula has an application to the optimal upper bound of a sum of restricted L^2-norms of the L^2-normalized newforms on certain quadratic extensions with prime level and bounded spectral parameter. For this we follow the methods in [Blo13].
References:
[Blo13] Valentin Blomer. On the 4-norm of an automorphic form. Journal of European Mathematical Society, 15:1825–1852, 2013.
[Ich08] A. Ichino. Trilinear forms and the central values of triple product L-functions. Duke Mathematical Journal, 145(2):281– 307, 2008.
[MV10] P. Michel and A. Venkatesh. The subconvexity problem for GL2. Publ. Math. Inst. Hautes Etudes Sci., (111):171–271, 2010.
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