Jacob’s ladders and the almost exact asymptotic representation of the Hardy-Littlewood integral

By J. Moser. 2009

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In this paper we introduce a nonlinear integral equation such that the system of global solutions to this equation represents the class of a very narrow beam as T → ∞ (an analog of the laser beam) and this sheaf of solutions leads to an almost-exact representation of the Hardy-Littlewood integral (1918). The accuracy of our result is essentially better than the accuracy of related results of Balasubramanian, Heath-Brown, and Ivic.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2cf32f728f9b29829c4dd369753b9c865443643d