Geodesic
On the distribution of integral points on cones
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 193-203

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Let $r_k(n)$ denote the number of representations of a positive integer $n$ as the sum of $k$ squares. We prove that $$ \sum_{n\le x}r^2_3(n)=Cx^2+O\Big(x^\frac32\big(\log x\big)^\frac72\Big), $$ where $C>0$ is a certain constant, and that $$ \sum_{n\le x}r^2_4(n)=32\zeta(3)x^3+O\Big(x^2\big(\log x\big)^\frac53\Big). $$ Bibl. 14 titles. 
@article{ZNSL_2010_383_a12,
     author = {O. M. Fomenko},
     title = {On the distribution of integral points on cones},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {193--203},
     publisher = {mathdoc},
     volume = {383},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a12/}
}
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EP  - 203
VL  - 383
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a12/
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ID  - ZNSL_2010_383_a12
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O. M. Fomenko. On the distribution of integral points on cones. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 25, Tome 383 (2010), pp. 193-203. http://geodesic.mathdoc.fr/item/ZNSL_2010_383_a12/