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Uniform distribution and lattice point counting

Part of: Algebraic number theory: global fields Geometry of numbers Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  09 April 2009

G. R. Everest
G. R. Everest
Affiliation:
School of MathematicsUniversity of East AngliaNorwich NR4 7TJ, UK
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Abstract

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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 generalisation 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 generalisation of a “heightcounting” formula of Györy and Pethö which itself was a generalisation of a theorem of Lang.

MSC classification

Secondary: 11H16: Nonconvex bodies 11M41: Other Dirichlet series and zeta functions 11R45: Density theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 1 , August 1992 , pp. 39 - 50
Copyright
Copyright © Australian Mathematical Society 1992

References

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