Maiti, Gopal2025-06-162025-06-162022-12122p.http://hdl.handle.net/10263/7557This thesis is under the supervision of Dr. Satadal GangulyIn this thesis, I described the notion of moments of L-functions in some families. Then I discussed some problems on estimating moments of L-functions. As applications, I showed some simultaneous non-vanishing and correlation results of certain product L-functions over number fields as well as function fields.enL- functionsSimultaneous non-vanishingGL(3)- Kuznetsov trace formulaCorrelation of quadratic Dirichlet L-functionsThesis