Probabilistic renormalization and analytic continuation

DOI10.1016/j.jnt.2022.03.007OpenAlexW3082903195WikidataQ114156537 ScholiaQ114156537MaRDI QIDQ2167497

Gunduz Caginalp, Bogdan Ion

Publication date: 25 August 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.13079

zbMATH Keywords

divergent seriesrenormalizationDirichlet series

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Convergence and divergence of series and sequences (40A05) Other Dirichlet series and zeta functions (11M41) Dirichlet series, exponential series and other series in one complex variable (30B50) Special methods of summability (40G99) Analytic continuation of functions of one complex variable (30B40)

Cites Work

• On polylogarithms, Hurwitz zeta functions, and the Kubert identities
• Chapter 6 of Ramanujan's second notebook
• Probability, information theory, and prime number theory
• Units in the modular function field. I. - II: A full set of units. - III: Distribution relations
• Distributions on toroidal groups
• Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
• A renormalization approach to the Riemann zeta function at \(-1,1+2+3+\dots\sim -1/12\).
• Uniform distributions on the natural numbers
• Fractal Geometry, Complex Dimensions and Zeta Functions
• The universal ordinary distribution
• Using Finitely Additive Probability: Uniform Distributions on the Natural Numbers
• Renormalization
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