On the Thue–Vinogradov Lemma
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 338-345
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We prove an extension of the Thue–Vinogradov lemma. This paper is another example for the application of the polynomial method, Rédei polynomials, and Stepanov's technique.
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Jozsef Solymosi. On the Thue–Vinogradov Lemma. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 338-345. http://geodesic.mathdoc.fr/item/TM_2021_314_a16/

[1] M. Aigner and G. M. Ziegler, “Representing numbers as sums of two squares”, Proofs from THE BOOK, Ch. 4, Springer, Berlin, 2018, 19–26 | DOI | MR

[2] Alon N., “Tools from higher algebra”, Handbook of combinatorics, v. 2, ed. by R.L. Graham, M. Grötschel, L. Lovász, Elsevier, Amsterdam, 1995, 1749–1783 | MR | Zbl

[3] Brauer A., Reynolds R., “On a theorem of Aubry–Thue”, Can. J. Math., 3 (1951), 367–374 | DOI | MR | Zbl

[4] Di Benedetto D., Solymosi J., White E., On the directions determined by a Cartesian product in an affine Galois plane, E-print, 2020, arXiv: 2001.06994 [math.CO]

[5] Hanson B., Petridis G., “Refined estimates concerning sumsets contained in the roots of unity”, Proc. London Math. Soc., 122:3 (2021), 353–358 ; arXiv: 1905.09134 [math.NT] | DOI | MR | Zbl

[6] Nagell T., Introduction to number theory, AMS Chelsea Publ. Ser., 163, AMS Chelsea Publ., Providence, RI, 2001 | MR

[7] Porcelli P., Pall G., “A property of Farey sequences, with applications to $q$th power residues”, Can. J. Math., 3 (1951), 52–53 | DOI | MR | Zbl

[8] Lacunary polynomials over finite fields, North Holland, Amsterdam, 1973 | MR

[9] S. A. Stepanov, “An elementary method in algebraic number theory”, Math. Notes, 24:3 (1978), 728–731 | DOI | MR | Zbl

[10] Szőnyi T., “On the number of directions determined by a set of points in an affine Galois plane”, J. Comb. Theory. Ser. A, 74:1 (1996), 141–146 | DOI | MR

[11] Szőnyi T., “Around Rédei's theorem”, Discrete Math., 208–209 (1999), 557–575 | MR

[12] Thue A., “Et par antydninger til en taltheoretisk methode”, Kra. Vidensk. Selsk. Forh., 7 (1902), 1–21; Selected mathematical papers of Axel Thue, Universitetsforlaget, Oslo, 1977, 57–75 | MR

[13] Vinogradov I.M., “On a general theorem concerning the distribution of the residues and non-residues of powers”, Trans. Amer. Math. Soc., 29 (1927), 209–217 | DOI | MR | Zbl

[14] I. M. Vinogradov, Elements of Number Theory, Dover Publ., New York, 1954 | MR | MR | Zbl