Number Theory

    

Sign Normalization for Higher Genus Curves in Generalized Riemann Hypothesis, and Generalized Birch and Swinnerton-Dyer Conjecture

Authors: John Yuk Ching Ting

This expository-styled paper contains interesting observations and conjectures about distribution of nontrivial zeros in L-functions; and [optional] use of Sign normalization when computing Hardy Z-function, including its relationship to Analytic rank and Symmetry type of L-functions. On the Sign normalization when applied to eligible L-functions, we posit its dependency on even-versus-odd Analytic ranks, degree of L-function, and the particular gamma factor present in functional equations for Genus 1 elliptic curves and higher Genus curves. The relevant mathematical arguments are postulated to satisfy Generalized Riemann hypothesis, and Generalized Birch and Swinnerton-Dyer conjecture. We explicitly mention their underlying proven/unproven hypotheses or conjectures.

Comments: 23 Pages. Generalized Riemann hypothesis and Generalized BSD conjecture

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Submission history

[v1] 2024-12-16 04:22:47
[v2] 2024-12-18 04:58:58

Unique-IP document downloads: 238 times

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