Kuznetsov and Mikheev Reply:

Petersson and Kuznetsov Trace Formulas

This article is an introduction to the Petersson trace formula and Kuznetsov trace formula, both of which are now important, standard techniques in analytic number theory. To illustrate their applications to modular forms, we will explain their role in a proof of subconvexity bounds for Rankin-Selberg L-functions L(s, f ⊗ g) on the critical line σ = 1/2, where here and throughout, we write s = ...

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Additive functionals and excursions of Kuznetsov processes

Let B be a continuous additive functional for a standard process (Xt)t∈R+ and let (Yt)t∈R be a stationary Kuznetsov process with the same semigroup of transition. In this paper, we give the excursion laws of (Xt)t∈R+ conditioned on the strict past and future without duality hypothesis. We study excursions of a general regenerative system and of a regenerative system consisting of the closure of...

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Exact Solutions to (3+1) Conformable Time Fractional Jimbo-miwa, Zakharov-kuznetsov and Modified Zakharov-kuznetsov Equations

Exact solutions to conformable time fractional (3+1)dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE. The resultant polynomial equation is solved by using algebrai...