Abstract
We prove some results concerning the distribution of quadratic residues and nonresidues in arithmetic progressions in the setting \( {{\mathbb{F}}_p}={{\mathbb{Z}} \left/ {{p\mathbb{Z}}} \right.} \), where p is a large prime.
Similar content being viewed by others
References
B.C. Berndt, R.J. Evans, and K.S. Williams, Gauss and Jacobi Sums, Can. Math. Soc. Ser. Monogr. Adv. Texts, Vol. 21, John Wiley & Sons, New York, 1998.
J. Friedlander and H. Iwaniec, Estimates for character sums, Proc. Am. Math. Soc., 119(2):365–372, 1993.
D.R. Heath-Brown, Burgess’s bounds for character sums, in J.M. Borwein et al. (Eds.), Number Theory and Related Fields: In Memory of Alf van der Poorter, Springer Proc. Math. Stat., Vol. 43, Springer, New York, 2013, pp. 199–213.
H. Iwaniec and E. Kowalski, Analytic Number Theory, Colloq. Publ., Am. Math. Soc., Vol. 53, Amer. Math. Soc., Providence, RI, 2004.
A.A. Karatsuba, Arithmetic problems in the theory of Dirichlet characters, Usp. Mat. Nauk, 63(4(382)):43–92, 2008.
I.M. Vinogradov, New approach to the estimation of a sum of values of χ(p + k), Izv. Akad. Nauk SSSR, Ser. Mat., 16:197–210, 1952.
I.M. Vinogradov, Improvement of an estimate for the sum of the values χ(p + k), Izv. Akad. Nauk SSSR, Ser. Mat., 17:285–290, 1953.
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Antanas Laurinčikas on the occasion of his 65th birthday
Rights and permissions
About this article
Cite this article
Justus, B. The distribution of quadratic residues and nonresidues in arithmetic progressions. Lith Math J 54, 142–149 (2014). https://doi.org/10.1007/s10986-014-9233-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10986-014-9233-0