Number Theory


Solving Incompletely Predictable Problems: Riemann Hypothesis, Polignac's and Twin Prime Conjectures

Authors: John Yuk Ching Ting

L-functions form an integral part of the 'L-functions and Modular Forms Database' with far-reaching implications. In perspective, Riemann zeta function is the simplest example of an L-function. Riemann hypothesis refers to the 1859 proposal by Bernhard Riemann whereby all nontrivial zeros of this function are conjectured to lie on the critical line. This proposal is equivalently stated in this research paper as all nontrivial zeros are conjectured to exactly match the 'Origin' intercepts of this function. Deeply entrenched in number theory, prime number theorem involves analysis of prime counting function for prime numbers. Solving Riemann hypothesis would enable complete delineation of this important theorem. Involving proposals on the magnitude of prime gaps and their associated sets of prime numbers, Twin prime conjecture deals with prime gap = 2 (representing twin primes) and is thus a subset of Polignac's conjecture which deals with all even number prime gaps = 2, 4, 6,... (representing prime numbers in totality except for the first prime number '2'). Both nontrivial zeros and prime numbers are Incompletely Predictable entities which allow us to employ our novel Virtual Container Research Method to solve the associated hypothesis and conjectures.

Comments: 69 Pages. Rigorous proofs for Riemann hypothesis, Polignac's and Twin prime conjectures

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Submission history

[v1] 2017-05-29 07:06:59
[v2] 2017-07-23 07:26:29
[v3] 2017-08-09 04:23:37

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