Our Interesting Journey with The Fascinating Mathematics of the Closed-form Formula of Riemann zeta and eta functions

  • Mulatu Lemma Professor
  • Agegnehu Atenaand Tilahun Muche
  • Wondimu Tekalign
Keywords: Sums of Powers of Complex Functions, Riemann zeta and Eta functions

Abstract

An explicit identity of sums of powers of complex functions presented via this a closed-form formula of Riemann zeta function produced at any given non-zero complex numbers. The closed-form formula showed us Riemann zeta function has no unique solution for any given non-zero complex numbers which means Riemann zeta function is entirely divergent. Infinitely many zeros of Riemann zeta function produced unfortunately those zeros also gives us non-zero values of Riemann zeta function. Among those zeros, some of them are zeros of Riemann hypothesis. The present paper also discussed on eta function(alternating Riemann zeta function) with exactly the same behavior as Riemann zeta function.

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Author Biographies

Mulatu Lemma, Professor

Department of Mathematics

College of Science and Technology

Savannah State University USA

Agegnehu Atenaand Tilahun Muche

College of Science and Technology

Savannah State University

Savannah, GA 3104, USA

Wondimu Tekalign

College of Science and Technology

Savannah State University

Savannah, GA 3104, USA

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Published
2021-02-22
How to Cite
Lemma, M., Muche, A. A., & Tekalign, W. (2021). Our Interesting Journey with The Fascinating Mathematics of the Closed-form Formula of Riemann zeta and eta functions. GPH - International Journal of Mathematics, 4(02), 01-10. Retrieved from http://gphjournal.org/index.php/m/article/view/371