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The properties of GL(2) automorphic L-functions - L-functions for classical modular forms and non-holomorphic Maass cusp forms - have played a very speical role in analytic number theory. In this talk we will study certain families of L-functions via Voronoi summation formulas and study their applications in two directions - Mazur, Rubin and Stein conjecture and the spectral first moment of L-functions. 
This talk combines two joint works with Diamantis, Hoffstein and Kiral, and with Hoffstein and Nastasescu.