Geodesic
Sums of Legendre symbols of polynomials of second degree over prime numbers
Izvestiya. Mathematics, Tome 12 (1978) no. 2, pp. 299-308 
A. A. Karatsuba. Sums of Legendre symbols of polynomials of second degree over prime numbers. Izvestiya. Mathematics, Tome 12 (1978) no. 2, pp. 299-308. http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a6/
@article{IM2_1978_12_2_a6,
     author = {A. A. Karatsuba},
     title = {Sums of {Legendre} symbols of polynomials of second degree over prime numbers},
     journal = {Izvestiya. Mathematics},
     pages = {299--308},
     year = {1978},
     volume = {12},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a6/}
}
TY  - JOUR
AU  - A. A. Karatsuba
TI  - Sums of Legendre symbols of polynomials of second degree over prime numbers
JO  - Izvestiya. Mathematics
PY  - 1978
SP  - 299
EP  - 308
VL  - 12
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a6/
LA  - en
ID  - IM2_1978_12_2_a6
ER  - 
%0 Journal Article
%A A. A. Karatsuba
%T Sums of Legendre symbols of polynomials of second degree over prime numbers
%J Izvestiya. Mathematics
%D 1978
%P 299-308
%V 12
%N 2
%U http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a6/
%G en
%F IM2_1978_12_2_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

Estimates are obtained for sums of Legendre symbols of a quadratic polynomial over prime numbers, these being nontrivial when the number of summands is greater than the three-fourths power of the modulus. Bibliography: 6 titles.

[1] Vinogradov I. M., Izbrannye trudy, AN SSSR, M., 1952 | MR | Zbl

[2] Vinogradov I. M., “Uluchshenie otsenki dlya summy znachenii $\chi(p+k)$”, Izv. AN SSSR. Ser. matem., 17 (1953), 285–290 | MR | Zbl

[3] Perelmuter G. I., “Otsenka odnoi summy s prostymi chislami”, Dokl. AN SSSR, 144:1 (1962), 48–51 | MR

[4] Karatsuba A. A., “Summy kharakterov s prostymi chislami”, Izv. AN SSSR. Ser. matem., 34 (1970), 299–321 | Zbl

[5] Karatsuba A. A., “O raspredelenii znachenii neglavnykh kharakterov”, Tr. Matem. instituta im. V. A. Steklova AN SSSR, 142, 1976, 156–164 | Zbl

[6] Karatsuba A. A., “Summy kharakterov s prostymi chislami, prinadlezhaschimi arifmeticheskoi progressii”, Izv. AN SSSR. Ser. matem., 35 (1971), 469–484 | Zbl