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The Mirror at One-Half

Posted by Nikitas Sotiropoulos on September 27, 2026

Uniform Asymptotics Zero-Free Regions Zeta Function

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A Small Taste from My New Book: Season 2 Episode 8

Posted by Nikitas Sotiropoulos on April 08, 2026

The point of controlled zero distance Well-spaced ordinate estimate

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Nikitas Sotiropoulos: Exploring math, code, and complex ideas.

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Primes rule the border: Why ζ(s) refuses to hit zero at Re(s)=1

This classical result, first proved by Hadamard and de la Vallée Poussin in the course of their proofs of the Prime Number Theorem, is obtained here through a direct analysis of the Euler product and the associated prime sums.

The Mirror at One-Half

Deep within the complex plane lies a hidden axis of symmetry where the secrets of the primes reside. Across the line every point reflects into a twin, binding the zeta function in a perfect mathematical duality. Welcome to another post where arithmetic, geometry and chaos meet.

How a Lemniscate Became an Elliptic Curve

The lemniscate of Bernoulli

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