References
- [1] BAKER, R. C.—HARMAN, G.—PINTZ, J.: The difference between consecutive primes, II, Proc. London Math. Soc. (3) 83 (2001), no. 3, 532–562.
- [2] BINGHAM, N. H.—GOLDIE, C. M.—TEUGELS, J. L.: Regular Variation.In: Encyclopedia of Mathematics and its Applications Vol. 27. Cambridge University Press, Cambridge, 1987.
- [3] DIACONIS, P.: The distribution of leading digits and uniform distribution mod 1, Ann. Probability 5 (1977), no. 1, 72–81.
- [4] ELIAHOU, S.—MASSÉ, B.—SCHNEIDER, D.: On the m.ntisa distribution of powers of natural and prime numbers, Acta Math. Hungar. 139 (1–2) (2013), 49–63.10.1007/s10474-012-0244-1
- [5] INGHAM, A. E.: The Distribution of Prime Numbers, Cambridge Univ. Press, New York, 1932.
- [6] KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences.In:Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974; Reprint: Dover Publications, Inc. Mineola, New York, 2006.
- [7] OHKUBO, Y.: On sequences involving primes, Unif. Distrib. Theory 6 (2011), no. 2, 221–238.
- [8] OHKUBO, Y.—STRAUCHI, O.: Distribution of leading digits of numbers, Unif. Distrib. Theory 11 (2016), no. 1, 23–45.
- [9] PAVLOV, A. I.: On distribution of fractions parts and Benford’s law Izv. Akad. Nauk SSSR Ser. Mat. 45 (1981), no. 4, 760–774. (In Russian)
- [10] ROSSER, J. B.—SCHOENFELD, L.: Approximate formulas for some functions of prime numbers Illinois J. Math. 6 (1962), 64–94.
- [11] SENETA, E.: Regularly Varying Functions.In: Lecture Notes in Math. Vol. 508. Springer-Verlag, Berlin, 1976.10.1007/BFb0079658
- [12] STRAUCH, O.—PORUBSKÝ, Š.: Distribution of Sequences: A Sampler. In: Series of the Slovak Academy of Sciences. Peter Lang, Frankfurt am Main, 2005.
- [13] WINTNER, A.: On the cyclical distribution of logarithms of the prime numbers,Quart. J. Math. 6 (1935), no.1, 65–68.