Submitted:
05 December 2025
Posted:
05 December 2025
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Abstract
The Extended, Generalized, and Grand Riemann Hypotheses are proved under a unified framework, which is based on the divisibility of entire functions expressed as absolutely convergent infinite products of polynomial factors, where the uniqueness of zero multiplicities plays a critical role. Consequently, the existence of Landau-Siegel zeros is excluded, thereby confirming the Landau-Siegel zeros conjecture.
Keywords:
extended Riemann hypothesis
; generalized Riemann hypothesis
; grand Riemann hypothesis
; Landau–Siegel zeros conjecture
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