View source for 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 $\mathbf R^n$.

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.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  F. Fricker,   "Einfürung in die Gitterpunktlehre" , Birkhäuser  (1981)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  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)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  A.Z. Walfisz,   "Gitterpunkte in mehrdimensionalen Kugeln" , PWN  (1957)</TD></TR></table>



====Comments====
Integral points are also called lattice points.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  P.M. Gruber,   C.G. Lekkerkerker,   "Geometry of numbers" , North-Holland  (1987)  pp. Sect. (iv)  (Updated reprint)</TD></TR></table>