Number Theory

    

On the L-Functions from Generalized Riemann Hypothesis, Birch and Swinnerton-Dyer Conjecture, and the Prime Numbers from Polignac's and Twin Prime Conjectures

Authors: John Yuk Ching Ting

We analyze L-functions of elliptic curves (and apply Sign normalization) which support simplest version of Birch and Swinnerton-Dyer conjecture to be true. Dirichlet eta function (proxy function for Riemann zeta function as generating function for all nontrivial zeros) and Sieve of Eratosthenes (generating algorithm for all prime numbers) are essentially infinite series. We apply infinitesimals to their outputs. Riemann hypothesis asserts the complete set of all nontrivial zeros from Riemann zeta function is located on its critical line. It is proven to be true when usefully regarded as an Incompletely Predictable Problem. The complete set with derived subsets of Odd Primes contain arbitrarily large number of elements and satisfy Prime number theorem for Arithmetic Progressions, Generic Squeeze theorem and Theorem of Divergent-to-Convergent series conversion for Prime numbers. Having these theorems being satisfied, Polignac's and Twin prime conjectures are separately proven to be true when usefully regarded as Incompletely Predictable Problems.

Comments: 64 Pages. LMFDB input on BSD conjecture, Riemann hypothesis, Polignac's and Twin prime conjectures

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Submission history

[v1] 2024-07-22 04:02:59
[v2] 2024-08-14 07:36:36

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