Alexander Vladimirovich Kuznetsov

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 = ...

Dedicated to the Memory of Vadim Kuznetsov

Zhedanov’s algebra AW (3) is considered with explicit structure constants such that the first generator becomes the Askey-Wilson second order q-difference operator in the basic representation. The faithfulness of this representation is proved. Some explicit aspects of the double affine Hecke algebra (DAHA) related to symmetric and nonsymmetric AskeyWilson polynomials are presented and proved wi...

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...

Alexander Ogilvy

Alexander M

As a former student of Professor Ostrowski—one of his last— I am delighted to recall here the life and work of one of the great mathematicians of the 20th century. Needless to say that, in view of Ostrowski’s immense and vastly diverse mathematical legacy, this can be done only in a most summary fashion. Further literature on Ostrowski can be found in some of the references at the end of this a...