A monotonicity property of Riemann’s $${\varvec{\xi }}$$ ξ function along certain curves

Gajendra Singh ()
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Gajendra Singh: Jai Narain Vyas University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 262-265

Abstract: Abstract In this paper, we prove that the modulus of Riemann $$\xi $$ ξ function is strictly increasing (respectively, strictly decreasing) in the zero-free right (respectively, left) half-plane along every curve belonging to a particular family. We also present a reformulation of the Riemann Hypothesis.

Keywords: Riemann zeta function; Riemann $$\xi $$ ξ function; Monotonicity; Riemann hypothesis; 11M06; 11M26 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00476-1

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