3 publications
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Binomially Regularized Riemann Zeta FunctionBy Lukasz Andrzej Glinka
Abstract: In this article, the most essential part of the binomial regularization of the Riemann zeta function, initiated through the author in an earlier book, is presented. The idea of the method arises from convergence of the negative binomial series determined in the standard sense of the infinite series theory. Meanwhile, the obtained result involves a remarkable series expansion of the Riemann zeta function in terms of the generalized Newton binomial …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 2, Issue 1, 2015 · pp. 1–8 Read article →
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On the Riemann Hypothesis in The Light of The Littlewood Criterion of EquivalenceBy Lukasz Andrzej Glinka
Abstract: In 1859, Riemann extended the Euler study onto the case of a complex variable according to then new Cauchy's complex analysis. According to his point of view, all non-trivial zeros of the Riemann zeta function are located on the critical line s=1/2+it, where t is a real number. In 1912, Littlewood presented the equivalence criterion for the Riemann Hypothesis based on the Mertens function. In this paper, the Riemann Hypothesis …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 1, Issue 2, 2014 · pp. 26–35 Read article →
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On the Formula for Distribution of Prime NumbersBy Lukasz Andrzej Glinka
Abstract: The detailed derivation of the distribution of prime numbers, the research result originally presented in the 2013’ monograph Study of Analytic Number Theory: Riemann’s Hypothesis and Prime Number Theorem with Addendum on Integer Partitions published with Cam- bridge International Science Publishing, is once again presented in this paper with the purpose to give an insight to unfamiliar authors.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 1, Issue 1, 2014 · pp. 16–19 Read article →