Geodesic
Sums of Legendre symbols of polynomials of second degree over prime numbers
Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 299-308.

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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. 
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     title = {Sums of {Legendre} symbols of polynomials of second degree over prime numbers},
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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/

[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