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Critical Line Zeros & Numerical Verification Beyond 10^13
Notes on Turing's method, Odlyzko–Schönhage FFT evaluations, and practical precision bottlenecks when computing Hardy's Z-function.
Prime Gaps, Cramér's Conjecture, and Elementary Sieve Bounds
Comparing heuristic probabilistic models for maximal prime gaps against recent Maynard–Tao small-gap refinements.
Trigonometric Substitutions & Convexity in High School Olympiad Inequalities
Collecting clean problems where Jensen's inequality or trigonometric parameterization simplifies symmetric three-variable bounds.
Euler Product Convergence on Re(s) = 1: Common Misconceptions
Why conditional convergence of the Euler product along the 1-line does not follow trivially from absolute convergence for Re(s) > 1.
Recommended Reading: Edwards, Titchmarsh, and Introductory Texts
A curated path from undergraduate complex analysis to Riemann's 1859 memoir and modern analytic number theory references.