Symmetry argument for the Riemann hypothesis, universality & broken symmetry
by Scott Allen

Abstract:

Upon careful re-examination of Riemann’s original work in the analytic continuation of the zeta function throughout the complex plane in general, and across the critical strip in particular, a natural invariant-symmetry principle and identity is derived, showing the hallmark characteristics of universality in the asymptotic limit. This invariant identity can be compared to Pitkänen and Castro, Mahecha et al. through the non-orthogonal coherent states, which have intriguing connections to the so-called Berry phase or Wess-Zumino term as described through an action in the non-linear sigma model revealing potential consequences to Riemann’s Hypothesis (RH). While theirs’ and others’ work is primarily based on the Hilbert & Polya’s conjecture as represented in supersymmetric quantum theory, conformal and scale invariance, 1/f noise, etc., the approach taken here is not based on any particular formalism as applied to operator or spectral theory; nor does it depend on analogues of analytic number theory to chaos theory or physics in general, requiring little more than basic complex analysis and Cauchy’s Residue theorem pertaining to the zeta function itself.


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