Geodesic
Small Solutions of the Congruence ax2 + by2 ≡ c(mod k)
Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 311-320

Voir la notice de l'article provenant de la source Cambridge University Press

In 1957, Mordell [3] provedTheorem. If p is an odd prime there exist non-negative integers x, y ≤ A p3/4 log p, where A is a positive absolute constant, such that (1.1) provided (abc, p) = 1.Recently Smith [5] has obtained a sharp asymptotic formula for the sum where r(n) denotes the number of representations of n as the sum of two squares. 
Williams, Kenneth S. Small Solutions of the Congruence ax2 + by2 ≡ c(mod k). Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 311-320. doi: 10.4153/CMB-1969-039-0
@article{10_4153_CMB_1969_039_0,
     author = {Williams, Kenneth S.},
     title = {Small {Solutions} of the {Congruence} ax2 + by2 \ensuremath{\equiv} c(mod k)},
     journal = {Canadian mathematical bulletin},
     pages = {311--320},
     year = {1969},
     volume = {12},
     number = {3},
     doi = {10.4153/CMB-1969-039-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-039-0/}
}
TY  - JOUR
AU  - Williams, Kenneth S.
TI  - Small Solutions of the Congruence ax2 + by2 ≡ c(mod k)
JO  - Canadian mathematical bulletin
PY  - 1969
SP  - 311
EP  - 320
VL  - 12
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-039-0/
DO  - 10.4153/CMB-1969-039-0
ID  - 10_4153_CMB_1969_039_0
ER  - 
%0 Journal Article
%A Williams, Kenneth S.
%T Small Solutions of the Congruence ax2 + by2 ≡ c(mod k)
%J Canadian mathematical bulletin
%D 1969
%P 311-320
%V 12
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-039-0/
%R 10.4153/CMB-1969-039-0
%F 10_4153_CMB_1969_039_0

[1] 1. Estermann, T., On Kloosterman's Sum. Mathematika 8 (1961) 83–86. Google Scholar

[2] 2. Estermann, T., A new application of the Hardy-Littlewood-Kloostermann Method. Proc. Lond. Math. Soc. 12 (1962) 425–444. Google Scholar

[3] 3. Mordell, L. J., On the number of solutions in incomplete residue sets of quadratic congruences. Archiv der Math. 8 (1957) 153–157. Google Scholar

[4] 4. Rademacher, H., Lectures on Elementary Number Theory. (Blaisdell, 1964) 93. Google Scholar

[5] 5. Smith, R. A., The circle problem in an arithmetic progression. Canad. Math. Bull. 11 (1968) 175–184. Google Scholar

[6] 6. Tietäväinen, A., On the trace of a polynomial over a finite field. Ann. Univ. Turku., Ser. Al, 87 (1966) 3–7. Google Scholar

[7] 7. Tietäväinen, A., On non-residues of a polynomial. Ann. Univ. Turku., Ser. Al, 94 (1966) 3–6. Google Scholar

[8] 8. Weil, A., On some exponential sums. Proc. Nat. Acad. Sci. (U.S.A.) 34 (1948) 204–207. Google Scholar

Cité par Sources :