Closed-form formula of Riemann zeta function and eta function for all\n non-zero given complex numbers via sums of powers of complex functions to\n disprove Riemann Hypothesis

2019/11/22 by Dagnachew Jenber Negash, Negash, Dagnachew Jenber
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Numerical Methods and Algorithms #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1911.10934

openalex publication_date 2019/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Series representations for the Stieltjes constants

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