Discrepancy estimates for a class of normal numbers

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1. [1] A. S. Besicovitch, The asymptotic distribution of the numerals in the decimal representation of the squares of the natural numbers, Math. Z. 39 (1935), 146-156. Zbl0009.20002
2. [2] D. G. Champernowne, The construction of decimals normal in the scale of ten, J. London Math. Soc. 8 (1933), 254-260. Zbl0007.33701
3. [3] H. Davenport and P. Erdős, Note on normal decimals, Canad. J. Math. 4 (1952), 58-63. Zbl0046.04902
4. [4] L.-K. Hua, Additive Theory of Prime Numbers, Transl. Math. Monographs 13, Amer. Math. Soc., Providence, Rhode Island, 1965. Zbl0192.39304
5. [5] A. A. Karatsuba, Foundations of Analytic Theory of Numbers, 2nd ed., Nauka, 1983 (in Russian). 
6. [6] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York 1974. Zbl0281.10001
7. [7] L. Mirsky, A theorem on representations of integers in the scale of r, Scripta Math. 15 (1974), 11-12. Zbl0034.17102
8. [8] Y.-N. Nakai and I. Shiokawa, A class of normal numbers, Japan. J. Math. 16 (1990), 17-29. 
9. [9] Y.-N. Nakai and I. Shiokawa, A class of normal numbers II, in: Number Theory and Cryptography, J. H. Loxton (ed.), London Math. Soc. Lecture Note Ser. 154, Cambridge Univ. Press, 1990, 204-210. 
10. [10] J. Schiffer, Discrepancy of normal numbers, Acta Arith. 47 (1986), 175-186. Zbl0556.10036
11. [11] J. Schoißengeier, Über die Diskrepanz von Folgen (αbⁿ), Sitzungsber. Öst. Akad. Wiss. Math.-Natur. Kl. Abt. II 187 (1978), 225-235. 
12. [12] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford Univ. Press, 1951. Zbl0042.07901
13. [13] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Math. 80, Cambridge Univ. Press, London 1981. 
14. [14] I. M. Vinogradov, The Method of Trigonometric Sums in Number Theory, Nauka, 1971 (in Russian). Zbl0229.10020

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