Geodesic
Difference Sets and Positive Exponential Sums. II: Cubic Residues in Cyclic Groups
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 145-151.

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

By constructing suitable nonnegative exponential sums, we give upper bounds on the cardinality of any set $B_q$ in cyclic groups $\mathbb Z_q$ such that the difference set $B_q-B_q$ avoids cubic residues modulo $q$. 
@article{TM_2021_314_a7,
     author = {M\'at\'e Matolcsi and Imre Z. Ruzsa},
     title = {Difference {Sets} and {Positive} {Exponential} {Sums.} {II:} {Cubic} {Residues} in {Cyclic} {Groups}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {145--151},
     publisher = {mathdoc},
     volume = {314},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_314_a7/}
}
TY  - JOUR
AU  - Máté Matolcsi
AU  - Imre Z. Ruzsa
TI  - Difference Sets and Positive Exponential Sums. II: Cubic Residues in Cyclic Groups
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2021
SP  - 145
EP  - 151
VL  - 314
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2021_314_a7/
LA  - ru
ID  - TM_2021_314_a7
ER  - 
%0 Journal Article
%A Máté Matolcsi
%A Imre Z. Ruzsa
%T Difference Sets and Positive Exponential Sums. II: Cubic Residues in Cyclic Groups
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2021
%P 145-151
%V 314
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2021_314_a7/
%G ru
%F TM_2021_314_a7
Máté Matolcsi; Imre Z. Ruzsa. Difference Sets and Positive Exponential Sums. II: Cubic Residues in Cyclic Groups. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 145-151. http://geodesic.mathdoc.fr/item/TM_2021_314_a7/

[1] Cohen S.D., “Clique numbers of Paley graphs”, Quaest. math., 11:2 (1988), 225–231 | DOI | MR | Zbl

[2] M. R. Gabdullin, “Sets in $\mathbb Z_m$ whose difference sets avoid squares”, Sb. Math., 209:11 (2018), 1603–1610 | DOI | MR | Zbl

[3] Matolcsi M., Ruzsa I.Z., “Difference sets and positive exponential sums. I: General properties”, J. Fourier Anal. Appl., 20:1 (2014), 17–41 | DOI | MR | Zbl

[4] Vaughan R.C., The Hardy–Littlewood method, Cambridge Tracts Math., 125, 2nd ed., Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl