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On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, II (Constructive Bounds)


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[1] BURGESS, D. A.: On character sums and primitive roots, Proc. London Math. Soc. 12 (1962), no. 3, 179–192.10.1112/plms/s3-12.1.179Search in Google Scholar

[2] DARTYGE, C.—GYARMATI, K.—SÁRKÖZY, A.: On irregularities of distribution of binary sequences relative to arithmetic progressions, I. (General results), Unif. Distrib. Theory 12 (2017), no. 1, 55–67.10.1515/udt-2017-0004Search in Google Scholar

[3] DAVENPORT, H.—ERDŐS, P.: The distribution of quadratic and higher residues, Publ. Math. Debrecen 2 (1952), 252–265.10.5486/PMD.1952.2.3-4.18Search in Google Scholar

[4] ERDŐS, P.—SÁRKÖZY, A.: Some solved and unsolved problems in combinatorial number theory, Math. Slovaca 28 (1978), 407–421.Search in Google Scholar

[5] GONG, K.: An elementary approach to character sums over multiplicative subgroups, Integers 16 (2016), #A13.Search in Google Scholar

[6] MATOUŠEK, J.—SPENCER, J.: Discrepancy in arithmetic progression, J. Amer. Math. Soc. 9 (1996), 195–204.10.1090/S0894-0347-96-00175-0Search in Google Scholar

[7] MAUDUIT, C.—SÁRKÖZY, A.: On finite pseudorandom binary sequences, I. Measure of pseudorandomness, the Legendre symbol, Acta Arith. 82 (1997), 365–377.10.4064/aa-82-4-365-377Search in Google Scholar

[8] MAUDUIT, C.—SÁRKÖZY, A.: On finite pseudorandom binary sequences, II. The Champernowne, Rudin–Shapiro, and Thue–Morse sequences, a further construction, J. Number Theory 73 (1998), 256–276.10.1006/jnth.1998.2286Search in Google Scholar

[9] MONTGOMERY, H. L.—VAUGHAN, R. C.: Mean values of character sums, Canad. J. Math. 31 (1979), no. 3, 470–487.10.4153/CJM-1979-053-2Search in Google Scholar

[10] PÓLYA, G.: Über die Verteilung der quadratischen Reste und Nichtreste, Göttinger Nachrichten 1918, 21–29.Search in Google Scholar

[11] QUEFFÉLEC, M.: Substitution Dynamical Systems—Spectral Analysis. In: Lecture Notes in Math. Vol. 1294, Springer-Verlag, Berlin, 1987.10.1007/BFb0081890Search in Google Scholar

[12] ROTH, K. F.: Remark concerning integer sequences, Acta Arith. 9 (1964), 257–260.10.4064/aa-9-3-257-260Search in Google Scholar

[13] RUDIN, W.: Some theorems on Fourier coefficients, Proc. Amer. Math. Soc. 10 (1959), 855–859.10.1090/S0002-9939-1959-0116184-5Search in Google Scholar

[14] SÁRKÖZY, A.: Some remarks concerning irregularities of distribution of sequences of integers in arithmetic progressions, IV, Acta Math. Acad. Sci. Hungar. 30(1-2) (1977), 155–162.10.1007/BF01895660Search in Google Scholar

[15] SHAPIRO, H. S.: Extremal Problems for Polynomials and Power Series. Doctoral Thesis, M. I. T., Massachusetts Institute of Technology, ProQuest LLC, Ann Arbor, MI, 1953.Search in Google Scholar

[16] VINOGRADOV, A. I.: On the symmetry property for sums with Dirichlet characters, Izv. Akad. Nauk UZSR, Ser. Fiz.-Mat. Nauk 1965 (1965), no. 1, 21–27. (In Russian)Search in Google Scholar

[17] WINTERHOF, A.: Some Estimates for Character Sums and Applications, Designs, Codes and Cryptography 22 (2001), 123–131.10.1023/A:1008300619004Search in Google Scholar

[18] ZHAO, L.: Burgess bound for character sums, January 2007, http://www.researchgate.net/publication/237203641Search in Google Scholar

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