Publications

  1. Integers free of prime divisors from an interval, I, Acta Arithmetica 98 (2001), 117-131. 
  2. Integers free of prime divisors from an interval, II, Acta Arithmetica 104 (2002), 309-343.
  3. Integers with dense divisors, Journal of Number Theory 108 (2004), 1-17.
  4. Integers with dense divisors 2, Journal of Number Theory 108 (2004), 18-28.
  5. On a question of Balazard and Saias related to the Riemann hypothesis, Advances in Mathematics, 208 (2007), 905-908.
  6. The distribution functions of σ(n)/n and n/φ(n), Proceedings of the American Mathematical Society, 135 (2007), 2677-2681.
  7. The limiting distribution of the divisor function, Journal of Number Theory 129 (2009), 1432-1442.
  8. Zeros of Dirichlet series with periodic coefficients (with Eric Saias), Acta Arithmetica 140.4 (2009), 335-344.
  9. On the solutions of σ(n)=σ(n+k), Journal of Integer Sequences 14 (2011), no. 5, Article 11.5.5, 7pp.
  10. On a conjecture of Adiga and Ramaswamy, International Journal of Mathematical Analysis 5 (2011), no. 21-24, 1063-1066.
  11. The distribution functions of σ(n)/n and n/φ(n), II, Journal of Number Theory 132 (2012), 2907-2921.
  12. On the diophantine equation Π xi = Σ xi , Integers 12 (2012), A57, 8 pp.
  13. On the sum of two almost periodic functions (with Eric Saias), Annales des sciences mathématiques du Québec 36 (2012), 231-234.
  14. Some applications of the double large sieve (with Roger Baker), Monatshefte für Mathematik 170 (2013), 261-304.
  15. Piatetski-Shapiro sequences (with Roger Baker, William Banks, Jörg Brüdern, Igor Shparlinski), Acta Arithmetica 157 (2013), 37-68. [arXiv:1203.5884]
  16. A ternary Diophantine inequality over primes (with Roger Baker),  Acta Arithmetica 162 (2014), 159-196.
  17. Integers with dense divisors 3, Journal of Number Theory 142 (2014), 211-222.
  18. Practical numbers and the distribution of divisors, The Quarterly Journal of Mathematics 66 (2015), 743-758, [arXiv:1405:2585]
  19. Integers with large practical component, Publicationes Mathematicae Debrecen 87 (2015), no. 3-4, 439-447, [arXiv:1411.6974]
  20. On the degrees of polynomial divisors over finite fields, Math. Proc. Cambridge Philos. Soc. 161 (2016), no. 3, 469–487. [arXiv:1507.01920]
  21. On integers for which Xn-1 has a divisor of every degree (with Carl Pomerance and Lola Thompson), Acta Arith. 175 (2016), no. 3, 225–243. [arXiv:1511:03357]
  22. An explicit polynomial analogue of Romanoff's theorem (with Igor Shparlinski), Finite Fields Appl. 44 (2017), 22–33.[arXiv:1510.08991]
  23. A sieve problem and its application, Mathematika 63 (2017), no. 1, 213-229. [arXiv:1605.05204]
  24. The practicality of shifted primes (with Victor Guo), Integers 18 (2018), A93, 7 pp.
  25. On the constant factor in several related asymptotic estimates, Math. Comp. 88 (2019), no. 318, 1883–1902. [arXiv:1705.06349]
  26. Set partitions without blocks of certain sizes (with Joshua Culver), European J. Combin. 84 (2020), 103041, 10 pp. [arXiv:1806.02316]
  27. The constant factor in the asymptotic for practical numbers, Int. J. Number Theory, 16 (2020), no. 3, 629-638. [arXiv:1906.07819]
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