38 citations · 140 across the 60 of their papers we have counts for
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Generalizations (in the spirit of Koshliakov) of some formulas from Ramanujan's Lost Notebook
Pedro Ribeiro, Semyon Yakubovich
In his lost notebook, Ramanujan recorded beautiful identities. These include earlier versions of Koshliakov's formula for the divisor function and the transformation formula for th…
Certain Extensions of Results of Siegel, Wilton and Hardy
Pedro Ribeiro, Semyon Yakubovich
Recently, Dixit et al. established a very elegant generalization of Hardy's Theorem concerning the infinitude of zeros that the Riemann zeta function possesses at its critical line…
Delicacy of the Riemann hypothesis and certain subsequences of superabundant numbers
Sadegh Nazardonyavi, Semyon Yakubovich
Robin's theorem is one of the ingenious reformulation of the Riemann hypothesis (RH). It states that the RH is true if and only if for all where $σ(n…
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…