View source for Integral points, distribution of

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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i051/i051600/i0516001.png" />.

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>