Geodesic
Note on Integers Representable by Binary Quadratic Forms
Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 123-125

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

Let B be the set of positive integers prime to d which are representable by some primitive, positive, integral binary quadratic form of discriminant d. It is the purpose of this note to show that the following asymptotic estimate for the number of integers in B less than or equal to x can be proved using only elementary arguments: (1) where c1 is the positive constant given in (17) below. (Using the deeper methods of complex analysis James [2] has proved this result with the error term ((log x)-1/2) replacing ((log log x)-1). Heupel [1] using a transcendental method as in James [2] improved this to ((log x)-1).) 
Williams, Kenneth S. Note on Integers Representable by Binary Quadratic Forms. Canadian mathematical bulletin, Tome 18 (1975) no. 1, pp. 123-125. doi: 10.4153/CMB-1975-022-6
@article{10_4153_CMB_1975_022_6,
     author = {Williams, Kenneth S.},
     title = {Note on {Integers} {Representable} by {Binary} {Quadratic} {Forms}},
     journal = {Canadian mathematical bulletin},
     pages = {123--125},
     year = {1975},
     volume = {18},
     number = {1},
     doi = {10.4153/CMB-1975-022-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-022-6/}
}
TY  - JOUR
AU  - Williams, Kenneth S.
TI  - Note on Integers Representable by Binary Quadratic Forms
JO  - Canadian mathematical bulletin
PY  - 1975
SP  - 123
EP  - 125
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-022-6/
DO  - 10.4153/CMB-1975-022-6
ID  - 10_4153_CMB_1975_022_6
ER  - 
%0 Journal Article
%A Williams, Kenneth S.
%T Note on Integers Representable by Binary Quadratic Forms
%J Canadian mathematical bulletin
%D 1975
%P 123-125
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-022-6/
%R 10.4153/CMB-1975-022-6
%F 10_4153_CMB_1975_022_6

[1] 1. Heupel, W., Die Verteilung der gangen Zahlen, die durch quadratische Formen dargestellt werden. Archiv. der. Math., 19 (1968), 162-166. Google Scholar

[2] 2. James, R. D., The distribution of integers represented by quadratic forms, Amer. J. Math., 60 (1938), 737-744. Google Scholar

[3] 3. Landau, E., Primzahlen, Chelsea Publishing Co., N.Y. (1953), second edition. Google Scholar

[4] 4. Pall, G., The distribution of integers represented by binary quadratic forms, Bull. Amer. Math. Soc, (1943), 447-449. Google Scholar

[5] 5. Rieger, G. J., Zahlentheoretische Anwendung eines Taubersatzes mit Restgied, Math. Ann., 182 (1969), 243-248. Google Scholar

[6] 6. Rieger, G. J., Zum Satz von Landau über die Summe aus zwei Quadraten, Jour, für die reine und angewandte Math., 244 (1970), 198-200. Google Scholar

[7] 7. Selberg, A., An elementary proof of the prime number theorem for arithmetic progressions, Canad. J. Math., 2 (1950), 66-78. Google Scholar

[8] 8. Uchiyama, S., On some products involving primes, Proc. Amer. Math. Soc, 28 (1971), 629–630. Google Scholar

[9] 9. Wirsing, E., Elementare Beweise des Primzahlsatzes mit Restglied II, Jour, für die reine und angewandte Math., 214/215 (1964), 1-18. Google Scholar

Cité par Sources :