___

• Abercrombie, A. G., Beatty sequences and multiplicative number theory, Acta Arith., 70(3) (1995), 195–207. http://doi.org/10.4064/aa-70-3-195-207
• Abercrombie, A. G., Banks, W. D., Shparlinski, I. E., Arithmetic functions on Beatty sequences, Acta Arith. 136(1) (2009), 81–89. http://doi.org/10.4064/aa136-1-6
• Akbal, Y., A short note on some arithmetical properties of the integer part of αp, Turkish Journal of Mathematics, 43(3) (2019), 1253–1262. http://doi.org/10.3906/mat-1809-43
• Akbal, Y., A note on values of Beatty sequences that are free of large prime factors, Colloquium Mathematicum, 160(1) (2020), 53–64. http://doi.org/10.4064/cm7715-2-2019
• Kumchev, A. V., On sums of primes from Beatty sequences, Integers 8 (2008), A8, 12 pp.
• Banks, W. D., Shparlinski, I. E., Non-residues and primitive roots in Beatty sequences, Bull. Austral. Math. Soc., 73(3) (2006), 433–443. http://doi.org/10.1017/S0004972700035449
• Banks, W. D., Shparlinski, I. E., Short character sums with Beatty sequences, Math. Res. Lett., 13 (2006), 539–547. http://doi.org/10.4310/MRL.2006.v13.n4.a4
• Banks, W. D., Shparlinski, I. E., Prime numbers with Beatty sequences, Colloq. Math., 115(2) (2009), 147–157. http://doi.org/10.4064/cm115-2-1
• Banks, W. D., Shparlinski, I. E., Prime divisors in Beatty sequences, J. Number Theory, 123(2) (2007), 413–425. http://doi.org/10.1016/j.jnt.2006.07.011
• Banks, W. D., Güloğlu, A., Vaughan, R. C., Waring’s problem for Beatty sequences and a local to global principle, J. Theor. Nombres Bordeaux, 26(1) (2014), 1–16. http://doi.org/10.5802/jtnb.855
• Banks, W. D., G¨ulo˘glu, A., Nevans, C. W., Representations of integers as sums of primes from a Beatty sequence, Acta Arith., 130(3) (2007), 255–275. http://doi.org/10.4064/aa130-3-4
• Davenport, H., Multiplicative number theory, Third edition, Revised and with a preface by Hugh L. Montgomery, Graduate Texts in Mathematics, 74, Springer-Verlag, New York, 2000.
• Graham, S. W., Kolesnik, G., Van der Corput’s method of exponential sums, London Mathematical Society Lecture Note Series, 126, Cambridge University Press, Cambridge, 1991.
• Güloğlu, A., Nevans, C. W., Sums of multiplicative functions over a Beatty sequence, Bull. Aust. Math. Soc., 78(2) (2008), 327–334. http://doi.org/10.1017/S0004972708000853
• Harman, G., Primes in Beatty sequences in short intervals, Mathematika, 62(2) (2016), 572–586. http://doi.org/10.1112/S0025579315000376
• Harman, G., Primes in intersections of Beatty sequences, J. Integer Seq., 18(7) (2015), 12 p.
• Khinchin, A. Y., Zur metrischen Theorie der diophantischen Approximationen, Math. Z. 24(4) (1926), 706–714. http://doi.org/10.1007/BF01216806
• Koksma, J. F., Some Theorems on Diophantine Inequalities, Scriptum no. 5, Math. Centrmn Amsterdam, 1950.
• Li, H., Pan, H., Primes of the form ⌊αp + β⌋, J. Number Theory, 129(10) (2009), 2328–2334.
• Mirsky, L., The number of representations of an integer as the sum of a prime and a k-free integer, Amer. Math. Monthly, 56 (1949), 17–19. http://doi.org/10.1080/00029890.1949.11990233
• Roth, K. F., Rational approximations to algebraic numbers, Mathematika, 2 (1955), 1–20. http://doi.org/10.1112/S0025579300000644
• Roth, K. F., Corrigendum to “Rational approximations to algebraic numbers”, Mathematika, 2 (1955), 168.
• Montgomery, H. L., Vaughan, R. C., Multiplicative Number Theory I. Classical Theory, Cambridge University Press, Cambridge, 2007.
• Vaughan, R. C., The general Goldbach problem with Beatty primes, Ramanujan J., 34(3) (2014), 347–359. http://doi.org/10.1007/s11139-013-9501-3
• Vaughan, R. C., The Hardy-Littlewood Method, 2nd ed., Cambridge Univ. Press, 1997.
• Vinogradov, I. M. The Method of Trigonometrical Sums in the Theory of Numbers, Dover Publications, Inc., Mineola, NY, 2004.