References
- Beck, J. (2001). Randomness in lattice point problems. Discrete Math. 229(1–3): 29–55. DOI: 10.1016/S0012-365X(00)00200-4.
- Beck, J. (2010). Randomness of the square root of 2 and the giant leap. Part 1. Period. Math. Hungar. 60(2): 137–242. DOI: 10.1007/s10998-010-2137-9.
- Beck, J. (2011). Randomness of the square root of 2 and the giant leap. Part 2. Period. Math. Hungar. 62(2): 127–246. DOI: 10.1007/s10998-011-6127-3.
- Beck, J. (2014). Probabilistic Diophantine Approximation. Springer Monographs in Mathematics. Heidelberg: Springer.
- Berger, A., Hill, T. P., Rogers, E. (2017). Benford online bibliography. www.benfordonline.net
- Berndt, B. C., Kim., S., Zaharescu, C. (2018). The circle problem of Gauss and the divisor problem of Dirichlet—Still unsolved. Amer. Math. Monthly. 125(2): 99–114. DOI: 10.1080/00029890.2018.1401853.
- Cai, Z., Faust, M., Hildebrand, A. J., Li, J., Zhang, Y. (2019). Leading digits of Mersenne numbers. Exp. Math. (to appear). DOI: 10.1080/10586458.2018.1551162.
- Diaconis, P. (1977). The distribution of leading digits and uniform distribution mod 1. Ann. Probab. 5(1): 72–81. DOI: 10.1214/aop/1176995891.
- Drmota, M., Tichy, R. (1997). Sequences, Discrepancies and Applications. Lecture Notes in Mathematics. Berlin: Springer.
- Erdős, P. (1964). Problems and results on diophantine approximations. Compos. Math. 16: 52–65.
- Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. II, 2nd ed. New York–London–Sydney: John Wiley & Sons, Inc.
- Guy, R. (1988). The strong law of small numbers. Amer. Math. Monthly. 95(8): 697–712. DOI: 10.1080/00029890.1988.11972074.
- Hardy, G. H., Littlewood, J. E. (1922). Some problems of diophantine approximation: The lattice-points of a right-angled triangle. Proc. Lond. Math. Soc. 2(1): 15–36. DOI: 10.1112/plms/s2-20.1.15.
- Hecke, E. (1922). Über analytische Funktionen und die Verteilung von Zahlen mod. eins. Abh. Math. Sem. Univ. Hamburg. 1(1): 54–76. DOI: 10.1007/BF02940580.
- Hill, T. P. (1995). The significant-digit phenomenon. Amer. Math. Monthly. 102(4): 322–327. DOI: 10.1080/00029890.1995.11990578.
- Kesten, H. (1966). On a conjecture of Erdős and Szüsz related to uniform distribution mod 1. Acta Arith. 12(1): 193–212. DOI: 10.4064/aa-12-2-193-212.
- Kuipers, L., Niederreiter, H. (1974). Uniform Distribution of Sequences. New York–London–Sydney: Wiley-Interscience
- Ostrowski, A. (1927). Mathematische Miszellen. IX. Notiz zur Theorie der Diophantischen Approximationen. Jahresber. Dtsch. Math. Ver. 36: 178–180.
- Ostrowski, A. (1930). Mathematische Miszellen. XVI. Notiz zur Theorie der linearen Diophantischen Approximationen. Jahresber. Dtsch. Math. Ver. 39: 34–46.
- Raimi, R. A. (1976). The first digit problem. Amer. Math. Monthly. 83(7): 521–538. DOI: 10.1080/00029890.1976.11994162.
- Ross, K. A. (2011). Benford’s law, a growth industry. Amer. Math. Monthly. 118(7): 571–583.
- Weyl, H. (1916). Über die Gleichverteilung von Zahlen mod. Eins. Math. Ann. 77(3): 313–352. DOI: 10.1007/BF01475864.