Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 4, Tome 227 (1995), pp. 5-8
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G. V. Abramov; P. M. Vinnik. Computation of the number of representations of the elements of the ring $\mathbb Z/d\mathbb Z$ as a sum of squares. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 4, Tome 227 (1995), pp. 5-8. http://geodesic.mathdoc.fr/item/ZNSL_1995_227_a0/
@article{ZNSL_1995_227_a0,
author = {G. V. Abramov and P. M. Vinnik},
title = {Computation of the number of representations of the elements of the ring $\mathbb Z/d\mathbb Z$ as a~sum of squares},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {5--8},
year = {1995},
volume = {227},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_227_a0/}
}
TY - JOUR
AU - G. V. Abramov
AU - P. M. Vinnik
TI - Computation of the number of representations of the elements of the ring $\mathbb Z/d\mathbb Z$ as a sum of squares
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1995
SP - 5
EP - 8
VL - 227
UR - http://geodesic.mathdoc.fr/item/ZNSL_1995_227_a0/
LA - ru
ID - ZNSL_1995_227_a0
ER -
%0 Journal Article
%A G. V. Abramov
%A P. M. Vinnik
%T Computation of the number of representations of the elements of the ring $\mathbb Z/d\mathbb Z$ as a sum of squares
%J Zapiski Nauchnykh Seminarov POMI
%D 1995
%P 5-8
%V 227
%U http://geodesic.mathdoc.fr/item/ZNSL_1995_227_a0/
%G ru
%F ZNSL_1995_227_a0
The number of representations of the elements of the ring $\mathbb Z/d\mathbb Z$ as a sum of invertible squares is computed, provided that each square occurs in the sum no more than a fixed number of times. For prime $d$ an exhaustive answer is given in terms of the class number and the fundamental unit of the real quadratic field $\mathbb Q(\sqrt d)$. Bibliography: 5 titles.
