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2011 (Vol. 3, Issue: 1)
Article Information:

Using Infinite Series Convergence to Prove the Riemann Hypothesis

M.V. Atovigba
Corresponding Author:  M.V. Atovigba 

Key words:  Absolute convergence, convergence, critical line, distance, electrons, energy, mass, mean and mean deviation approach, quarks, Riemann zeta function, speed, zero
Vol. 3 , (1): 39-44
Submitted Accepted Published
2010 November, 08 2010 December, 02 2011 February, 15

The study attempts to prove the Riemann hypothesis by showing that the Riemann zeta function converges to zero and absolutely converges to 0. The work uses the mean and mean deviation approach of solving quadratic equations, in identifying the roots of an auxiliary energy equation of some second order homogeneous ordinary differential equation. The energy equation is brought about by simultaneously treating energy generation by electrons and quarks. A set of complex roots of the auxiliary equation takes the form of the set of analytic zeros s = + it of the Riemann zeta function ς(s). s varies partly as and partly as some t, t being a function of the mass (m) of particles and k distance (or frequency) achieved by the particle. The Riemann zeta function is treated as an infinite series which converges to 0 as t tends to infinity and which converges absolutely to 0 as t tends to infinity.
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  Cite this Reference:
M.V. Atovigba, 2011. Using Infinite Series Convergence to Prove the Riemann Hypothesis.  Research Journal of Mathematics and Statistics, 3(1): 39-44.
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ISSN (Online):  2040-7505
ISSN (Print):   2042-2024
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