Difference between revisions of "Integral points, distribution of"
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| − | Certain asymptotic formulas in analytic number theory for arithmetic functions that can be stated as answers to problems on the number of integral points (cf. [[Integral point|Integral point]]) in some manifolds, in the first instance, in homothetically-extending domains in the space | + | {{TEX|done}} |
| + | Certain asymptotic formulas in analytic number theory for arithmetic functions that can be stated as answers to problems on the number of integral points (cf. [[Integral point|Integral point]]) in some manifolds, in the first instance, in homothetically-extending domains in the space $\mathbf R^n$. | ||
Here the [[Circle problem|circle problem]] (C.F. Gauss) and the [[Divisor problems|divisor problems]] (P.G.L. Dirichlet) are classical (starting points) as well as their numerous generalizations. | Here the [[Circle problem|circle problem]] (C.F. Gauss) and the [[Divisor problems|divisor problems]] (P.G.L. Dirichlet) are classical (starting points) as well as their numerous generalizations. | ||
Latest revision as of 17:31, 30 April 2014
Certain asymptotic formulas in analytic number theory for arithmetic functions that can be stated as answers to problems on the number of integral points (cf. Integral point) in some manifolds, in the first instance, in homothetically-extending domains in the space $\mathbf R^n$.
Here the circle problem (C.F. Gauss) and the divisor problems (P.G.L. Dirichlet) are classical (starting points) as well as their numerous generalizations.
References
| [1] | F. Fricker, "Einfürung in die Gitterpunktlehre" , Birkhäuser (1981) |
| [2] | L.-K. Hua, "Abschätzungen von Exponentialsummen und ihre Anwendung in der Zahlentheorie" , Enzyklopaedie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen , 1 : 2 (1959) (Heft 13, Teil 1) |
| [3] | A.Z. Walfisz, "Gitterpunkte in mehrdimensionalen Kugeln" , PWN (1957) |
Comments
Integral points are also called lattice points.
References
| [a1] | P.M. Gruber, C.G. Lekkerkerker, "Geometry of numbers" , North-Holland (1987) pp. Sect. (iv) (Updated reprint) |
How to Cite This Entry:
Integral points, distribution of. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Integral_points,_distribution_of&oldid=32003
Integral points, distribution of. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Integral_points,_distribution_of&oldid=32003
This article was adapted from an original article by A.V. Malyshev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article