J Austral Math Soc Ser A 53 pp39--50, 1992.

Uniform Distribution and Lattice Point Counting

G. R. Everest

Abstract

A well-known theorem of Hardy and Littlewood gives a three-term asymptotic formula, counting the lattice points inside an expanding, right triangle. In this paper a generalization of their theorem is presented. Also an analytic method is developed which enables one to interpret the coefficients in the formula. These methods are combined to give a generalization of a "height counting" formula of Györy and Pethö which itself was a generalization of a theorem of Lang.

1991 AMS Subject Classification: 11H16, 11M41, 11R45

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Authors

G. R. Everest

School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK.