Binomially Regularized Riemann Zeta Function

Authors

  • Lukasz Andrzej Glinka Non-fiction Writer, Science Editor and Science Author

DOI:

https://doi.org/10.37591/rrdms.v2i1.204

Keywords:

Riemann zeta function, regularization methods, generalized Newton binomial coefficients, Taylor power series expansion, Bernoulli polynomials

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 coefficients and the Bernoulli polynomials which can be interesting from the point of view of further research of the Riemann zeta function and related problems, such like the Riemann hypothesis.

 

Cite this Article:
Lukasz Andrzej Glinka. Binomially Regularized Riemann Zeta Function. Research & Reviews: Discrete Mathematical Structures. 2015; 2(1): 1–8p.

Author Biography

  • Lukasz Andrzej Glinka, Non-fiction Writer, Science Editor and Science Author

    BIRTH DATA 5 October 1984, Poland

    PROFESSIONAL WEB-PAGES

    http://www.linkedin.com/in/laglinka

    http://www.academicroom.com/users/laglinka

    http://www.goodreads.com/author/show/5832296

    http://membership.sciencepublishinggroup.com/laglinka

    SUMMARY

    • Author. 2 science books and 1 book in humanities

    • Author. 42 science papers and manuscripts

    • Editor. Research & Reviews: Discrete Mathematical Structures (STM Journals, Consortium eLearning Network Private Ltd)

    • Editor. Review of Applied Physics (Science and Engineering Publishing Company)

    • Editor. Journal of Advances in Physics (Council for Innovative Research)

    • Editor. Science Journal of Applied Mathematics and Statistics (Science Publishing Group)

    • Editor. Applied Mathematics and Physics (Science and Education Publishing)

    • Attended 16 academic conferences, given 26 public presentations

    • Biography published by Marquis Who’s Who

    • Citations. More than 3 books and 75 papers of other authors

    EXPERIENCE

    • in 2013: IBM, Bratislava, Slovakia

    • in 2013: B.M. Birla Science Centre, Hyderabad, India

    • in 2011: TC Systems SA, Mendrisio, Switzerland

    • in 2010: Peoples’ Friendship University of Russia, Moscow, Russia

    • in 2009: B.M. Birla Science Centre, Hyderabad, India

    • in 2008: University of Udine, Udine, Italy

    • 2006-2008: Joint Institute for Nuclear Research, Dubna, Russia

    – in 2007: Centre de Physique Théorique de Marseille, Marseille, France

    – in 2007: University of Warsaw, Warsaw, Poland

    – in 2007: University of Wroclaw, Wroclaw, Poland

    – in 2006: Sołtan Institute for Nuclear Studies, Warsaw, Poland

    AUTHORED BOOKS

    L.A. Glinka (2013). Theorizing Emotions: A Brief Study of Psychological, Philosophical, and Cultural Aspects of Human Emotions. Cambridge International Science Publishing, 104 pages, ISBN-13: 978-1907343957. Information: www.cisp-publishing.com/acatalog/info_105.html

    L.A. Glinka (2013). Study of Analytic Number Theory: Riemann’s Hypothesis and Prime Number Theorem with Addendum on Integer Partitions. Cambridge International Science Publishing, 108 pages, ISBN-13: 978-1907343988. Information: www.cisp-publishing.com/acatalog/info_104.html

    L.A. Glinka (2012). Aethereal Multiverse: A New Unifying Theoretical Approach to Cosmology, Particle Physics, and Quantum Gravity. Cambridge International Science Publishing, 830 pages, ISBN-13: 978-1907343568. Information: www.cisp-publishing.com/acatalog/info_101.html

    CONTACT

    e-mail: [email protected]

    mobile phone: (+48) 660 019 237

References

Ferrar W.L. A Text-Book of Convergence. Oxford University Press; G.H. Hardy. 1938.

Divergent Series. Oxford University Press; K. Knopp. 1949.

Infinite Sequences and Series. Dover Publications;G.M. Fichtenholz. 1956.

Fichtenholz G.M. Infinite Series: Ramifications, Gordon & Breach. 1970. Trench W.F. Introduction to Real Analysis, Prentice Hall. 2002.

Graham L., Knuth D.E., and Patashnik O. Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley. 1994.

Glinka L.A. Study of Analytic Number Theory: Riemann’s Hypothesis and Prime Number Theorem with Addendum on Integer Partitions. Cambridge International Science Publishing.2014.

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Published

2015-04-28

Issue

Vol. 2 No. 1 (2015)

Section

Research Articles

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