Research ArticleOpen accessPhrase in the titleProof of Analytic Extension Theorem for Zeta Function Using Abel Transformation and Euler ProductMbaitiga ZacharieProblem statement: In the prime number the Riemann zeta function is unquestionable and undisputable one of the most important questions in mathematics whose many researchers are still trying to find answer to some unsolved problems such as Riemann Hypothesis. In this study we proposed a new method that proves the analytic extension theorem for zeta function. Approach: Abel transformation was … …Journal of Mathematics and Statistics, Vol. 6, Issue 3 · 30 Sep 2010 · 7,923 accessesView PDFCite
Research ArticleOpen accessIn the keywordsA Numerical Test on the Riemann Hypothesis with ApplicationsN. K. Oladejo, I. A. AdetundeProblem statement: The Riemann hypothesis involves two products of the zeta function ζ(s) which are: Prime numbers and the zeros of the zeta function ζ(s). It states that the zeros of a certain complex-valued function ζ (s) of a complex number s ≠ 1 all have a special form, which may be trivial or non trivial. Zeros at the negative … …Journal of Mathematics and Statistics, Vol. 5, Issue 1 · 31 Mar 2009 · 7,859 accessesView PDFCite
Research ArticleOpen accessIn the abstractEffects of Different Extraction Methods on the Quality of Peony Seed Oil and Its Emulsion PropertiesKang Li, Chao Du, Shuxian Pang et al.Peony seed oil, as a functional oil rich in ω-3 polyunsaturated fatty acids and natural antioxidant components, has its extraction process directly affecting the maintenance of bioactive substances and the added value of the product. In this analysis, the effects of wet milling-micronized continuous leaching method (MCI), solvent extraction (SE), soxhlet extraction (SOXE) and ethanol-assisted enzymatic hydrolysis (EAH) on the … …American Journal of Biochemistry and Biotechnology, Vol. 21, Issue 3 · 28 Jan 2026 · 1,955 accessesView PDFCite
Research ArticleOpen accessIn the abstractProof of Bernhard Riemann's Functional Equation using Gamma FunctionMbaïtiga ZacharieThis study shows the use of gamma function to prove the Riemann functional equation. Two approaches had been used to solve this problem: first the value of t in the definition of the gamma function had been changed to pi nu x if only if sigma is greater than zero in the complex plane. Secondly, the Poisson summation formula is … …Journal of Mathematics and Statistics, Vol. 4, Issue 3 · 30 Sep 2008 · 7,695 accessesView PDFCite