26 citations · 30 across the 8 of their papers we have counts for
8 papers
Sharper estimates for Chebyshev's functions and
Sadegh Nazardonyavi, Semyon Yakubovich
In this article we present some improved results for Chebyshev's functions and using the new zero-free region obtained by H. Kadiri and the calculated the first $10…
Superabundant numbers, their subsequences and the Riemann hypothesis
Sadegh Nazardonyavi, Semyon Yakubovich
Let σ(n) be the sum of divisors of a positive integer n. Robin's theorem states that the Riemann hypothesis is equivalent to the inequality σ(n)<e^γn\log\log n for all n>5040 (γis…
On the Yor integral and a system of polynomials related to the Kontorovich-Lebedev transform
Semyon Yakubovich
In this paper we establish different representations of the so-called Yor integral, which is one of the key ingredient in mathematical finance, in particular, to compute normalized…
A class of index transforms generated by the Mellin and Laplace operators
Semyon Yakubovich
Classical integral representation of the Mellin type kernel in terms of the Laplace integral gives an idea to construct a new class of non-convolution (index) transforms. Particula…
The Kontorovich-Lebedev transform as a map between -orthogonal polynomials
Ana F. Loureiro, S. Yakubovich
A slight modification of the Kontorovich-Lebedev transform is an automorphism on the vector space of polynomials. The action of this -transform over certain polynomial sequen…
On an inequality for the Riemann zeta-function in the critical strip
Sadegh Nazardonyavi, Semyon Yakubovich
By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |ζ(1-s)| <= |ζ(s)| in the strip 0< Re s<1/2,\ |\Im s| >= 12. More…