Professional Information

Area of Research

Number Theory

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. [PDF]
  9. On the solutions of σ(n)=σ(n+k), Journal of Integer Sequences 14 (2011), no. 5, Article 11.5.5, 7pp. [PDF]
  10. On a conjecture of Adiga and Ramaswamy, International Journal of Mathematical Analysis 5 (2011), no. 21-24, 1063-1066. [PDF]
  11. The distribution functions of σ(n)/n and n/φ(n), II, Journal of Number Theory 132 (2012), 2907-2921. [PDF]
  12. On the diophantine equation Π xi = Σ xi , Integers 12 (2012), A57, 8 pp. [PDF]
  13. On the sum of two almost periodic functions (with Eric Saias), Annales des sciences mathématiques du Québec 36 (2012), 231-234. [PDF]
  14. Some applications of the double large sieve (with Roger Baker), Monatshefte für Mathematik 170 (2013), 261-304. [PDF]
  15. Piatetski-Shapiro sequences (with Roger Baker, William Banks, Jörg Brüdern, Igor Shparlinski), Acta Arithmetica 157 (2013), 37-68. [PDF]
  16. A ternary Diophantine inequality over primes (with Roger Baker),  Acta Arithmetica 162 (2014), 159-196. [PDF]
  17. Integers with dense divisors 3, Journal of Number Theory 142 (2014), 211-222. [PDF]
  18. Practical numbers and the distribution of divisors, arXiv preprint. [PDF]
  19. Integers with large practical component, arXiv preprint. [PDF]