| viXra.org > Number Theory > viXra:2604.0079 |
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| viXra.org > Number Theory > viXra:2604.0079 |
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Number Theory |
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Authors: Payam Danesh
A Gamma—Bernoulli approach to the critical-line problem for the Riemann zeta function is developed. Starting from the Mellin—theta representation and the functional equation, one obtains explicit identities for the reflected Gamma quotient and for the regularization built into the Weierstrass product for Γ. On the Bernoulli side, the kernel (eu − 1)−1 is decomposed into its singular part and an analytic remainder, which yields a concrete zero-conditioned identity after continuation. The analysis shows that the harmonic divergence visible in raw finite Gamma products is a truncation phenomenon and therefore cannot by itself force Re(ρ) = 1/2. What remains is a coercive estimate which, if established, would convert the same mechanism into a critical-line theorem.
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[v1] 2026-04-21 23:49:01
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