Jacob's ladders and the tangent law for short parts of the Hardy-Littlewood integral

2009/06/03 by Jan Moser, Moser, Jan · 2 citations
Mathematics · #Algebraic and Geometric Analysis #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #math.CA

paper · pdf · doi:10.48550/arxiv.0906.0659

openalex publication_date 2009/06/03 · arxiv created 2010/02/04 · arxiv updated 2010/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The elementary geometric properties of the Jacob's ladders \cite7 lead to a class of new formulae for short parts of the Hardy-Littlewood integral. This class of formulae cannot be obtained by methods of Balasubramanian, Heath-Brown and Ivic.

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• Jacob's ladders and new orthogonal systems generated by Jacobi polynomials
• Jacob's ladders and the asymptotically approximate solutions of a nonlinear diophantine equation

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