2017/07/03 by Yochay Jerby, Jerby, Yochay
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Inequalities and Applications #math.GM
paper · pdf · doi:10.48550/arxiv.1707.01754
openalex publication_date 2017/07/03 · arxiv created 2017/08/30 · arxiv updated 2017/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1970, based on newly available empiric evidence, a remarkable monotonicity property for | ζ(z) | was conjectured by R. Spira. The ζ-monotonicity property can be written as follows: | ζ(x2 + y i ) | < | ζ ( x1 +y i )| \hspace0.5cm \textrm for any \hspace0.25cm x1 < x2 ≤ 0.5 \textrm and 6.29 <y. In this work we present an experimental study of the monotonicity conjecture, in the course of which new properties of ζ(z) are discovered. For instance, the spectrum of semi-limits λ(z) ⊂ ℝ and the core function C(z), which serves as a non-chaotic simplification of ζ(z) to the left of the critical line