Number Theory

   

On Exponential Decay and the Riemann Hypothesis

Authors: Jeffrey N. Cook

A Riemann operator is constructed in which sequential elements are removed from a decaying set by means of prime factorization, leading to a form of exponential decay with zero degeneration, referred to as the root of exponential decay. A proportionate operator is then constructed in a similar manner in terms of the non-trivial zeros of the Riemann zeta function, extending proportionately, mapping expectedly always to zero, which imposes a ratio of the primes to said zeta roots. Thirdly, a statistical oscillation function is constructed algebraically into an expression of the Laplace transform that links the two operators and binds the roots of the functions in such a manner that the period of the oscillation is defined (and derived) by the eigenvalues of one and the elements of another. A proof then of the Riemann hypothesis is obtained with a set of algebraic paradoxes that unmanageably occur for the single incident of any non-trivial real part greater or less than a rational one half.

Comments: 74 Pages. Fix a couple minor typos.

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Submission history

[v1] 2013-01-12 07:32:29
[v2] 2013-01-12 10:48:16
[v3] 2013-01-14 09:31:16
[v4] 2013-01-15 12:19:39
[v5] 2013-01-16 10:38:56
[v6] 2013-01-21 09:10:54
[v7] 2013-01-30 09:09:19
[v8] 2013-02-04 12:28:01
[v9] 2013-02-22 17:02:20
[vA] 2013-03-15 10:32:30
[vB] 2014-01-08 18:17:40
[vC] 2014-01-09 09:10:59
[vD] 2014-01-27 14:29:03

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