Publications

Journal Articles in Number Theory+

  1. A framework for discrete bilinear spherical averages and applications to \(\ell^p\)-improving estimates (with T. Anderson and E. Palsson). Colloquium Mathematicum 175 (2024), 55–76.
  2. Short interval results for powerfree polynomials over finite fields (with N. McNew and A. Park). International Journal of Number Theory 20 (2024), 867–892.
  3. Explicit bounds for large gaps between squarefree integers (with W. McCormick, N. McNew, A. Park, R. Scherr, and W. Ziehr). Journal of Number Theory 254 (2024), 336–357.
  4. Discrete maximal operators for surfaces of higher codimension (with T. Anderson and E. Palsson). (La) Matematica 1 (2022), 442–479.
  5. On the ergodic Waring-Goldbach problem (with T. Anderson, B. Cook and K. Hughes). Journal of Functional Analysis 282 (2022), Paper 109334, 39 pp.
  6. Hilbert transforms and the equidistribution of zeros of polynomials (with E. Carneiro, M. Das, A. Florea, A. Malik, M. Milinovich, C. Turnage-Butterbaugh, and J. Wang). Journal of Functional Analysis 281 (2021), Paper 109199, 25 pp.
  7. A hybrid of two theorems of Piatetski-Shapiro (with Zh. Petrov). Monatshefte für Mathematik 189 (2019), 355–376.
  8. Improved \(\ell^p\)-boundedness for integral \(k\)-spherical maximal functions (with T. Anderson, B. Cook and K. Hughes). Discrete Analysis 2018, Paper 10, 18 pp.
  9. On sums of powers of almost equal primes (with H. Liu). Journal of Number Theory 176 (2017), 344–364.
  10. The strong symmetric genus spectrum of abelian groups (with C. May and J. Zimmerman). Archiv der Mathematik (Basel) 108 (2017), 341–350.
  11. On the Waring-Goldbach problem for seventh and higher powers (with T. Wooley). Monatshefte für Mathematik 183 (2017), 303–310.
  12. On the Waring-Goldbach problem for eighth and higher powers (with T. Wooley). Journal of the London Mathematical Society (2) 93 (2016), 811–824.
  13. On sums of four squares of primes (with L. Zhao). Mathematika 62 (2016), 348–361.
  14. On the fractional parts of \(a^n/n\) (with J. Cilleruelo, F. Luca, J. Rué, and I. Shparlinski). Bulletin of the London Mathematical Society 45 (2013), 249–256.
  15. On the convergence of some alternating series. Ramanujan Journal 30 (2013), 101–116.
  16. Sums of almost equal squares of primes (with T. Li). Journal of Number Theory 132 (2012), 608–636.
  17. On sums of Ramanujan sums (with T.H. Chan). Acta Arithmetica 152 (2012), 1–10.
  18. Additive bases arising from functions in a Hardy field (with T.H. Chan and M. Wierdl). Acta Mathematica Hungarica 129 (2010), 263–276.
  19. On sums of squares of primes II (with G. Harman). Journal of Number Theory 130 (2010), 1969–2002.
  20. Sums of primes and squares of primes in short intervals (with J. Liu). Monatshefte für Mathematik 157 (2009), 335–363.
  21. A binary additive equation involving fractional powers. International Journal of Number Theory 5 (2009), 281–292.
  22. On sums of primes from Beatty sequences. Integers 8 (2008), #A08.
  23. On the irreducibility of a truncated binomial expansion (with M. Filaseta and D. Pasechnik). Rocky Mountain Journal of Mathematics 37 (2007), 455–464.
  24. On Weyl sums over primes and almost primes. Michigan Mathematical Journal 54 (2006), 243–268.
  25. Mean values of Dirichlet polynomials and applications to linear equations with prime variables (with S. Choi). Acta Arithmetica 123 (2006), 125–142.
  26. On sums of squares of primes (with G. Harman). Mathematical Proceedings of the Cambridge Philosophical Society 140 (2006), 1–13.
  27. On sums of three squares (with S. Choi and R. Osburn). International Journal of Number Theory 1 (2005), 161–173.
  28. The Waring–Goldbach problem for seventh powers. Proceedings of the American Mathematical Society 133 (2005), 2927–2937.
  29. On the Waring–Goldbach problem: Exceptional sets for sums of cubes and higher powers. Canadian Journal of Mathematics 57 (2005), 298–327.
  30. Quadratic equations with five prime unknowns (with S. Choi). Journal of Number Theory 107 (2004), 357–367.
  31. The distribution of prime ideals of imaginary quadratic fields (with G. Harman and P. Lewis). Transactions of the American Mathematical Society 356 (2004), 599–620.
  32. The difference between consecutive primes in an arithmetic progression. Quarterly Journal of Mathematics Oxford (2) 53 (2002), 479–501.
  33. Diophantine approximation by cubes of primes and an almost prime II (with J. Brüdern). Illinois Journal of Mathematics 45 (2001), 309–321.
  34. Diophantine approximation by cubes of primes and an almost prime. Rocky Mountain Journal of Mathematics 30 (2000), 961–980.
  35. The k-free divisor problem. Monatshefte für Mathematik 129 (2000), 321–327.
  36. A note on the 2k-th mean value of the Hurwitz zeta-function. Bulletin of the Australian Mathematical Society 60 (1999), 403–405.
  37. A Diophantine inequality involving prime powers. Acta Arithmetica 89 (1999), 311–330.
  38. On the distribution of prime numbers of the form \([n^c]\). Glasgow Mathematical Journal 41 (1999), 85–102.
  39. On an equation with prime numbers (with T. Nedeva). Acta Arithmetica 83 (1998), 117–126.
  40. On the Piatetski-Shapiro–Vinogradov theorem. Journal de Théorie des Nombres de Bordeaux 9 (1997), 11–23.
  41. An additive problem with prime numbers from a thin set (with D. Tolev). Acta Mathematica Hungarica 76 (1997), 31–43.
  42. On a system of two Diophantine equations with prime numbers. Comptes Rendus de l’Academie Bulgare des Sciences 49 (1996), 21–24.

 

Articles in Conference Proceedings and Other Publications

  1. Explicit bounds for large gaps between cubefree integers (with W. McCormick, N. McNew, A. Park, R. Scherr, and W. Ziehr). To appear in “Combinatorial and Additive Number Theory VI” (Proceedings of the CANT Workshops, New York, NY: May 2022 and May 2023), Springer.
  2. On a two-dimensional exponential sum. In “Combinatorial and Additive Number Theory IV” (Proceedings of the CANT Workshops, New York, NY: May 21-24, 2019 and June 1-5, 2020), Springer, 2021, pp. 371–383.
  3. Sieve methods and exponential sums: An interplay between combinatorics and harmonic analysis. In “Prime Numbers and Representation Theory” (Proceedings of the Workshops on Number Theory, Beijing: July 20–28, 2014 and July 16–31, 2015), Science Press, 2017, pp. 13–47.
  4. On Weyl sums over primes in short intervals. In “Number Theory: Arithmetic in Shangri-La” (Proceedings of the China–Japan Seminar on Number Theory, Shanghai: August 15–17, 2011), World Scientific, 2013, pp. 116–131.
  5. Estimation of the commodity flow of chlorine from storage data (with D. Howell, A. Kolesnikov, P. O’Neill, and M. Tiger). Journal of Transportation Security 5 (2012), 51–68.
  6. An invitation to additive prime number theory (with D. Tolev). Serdica Mathematical Journal 31 (2005), 1–74.
  7. On a binary Diophantine inequality involving prime powers (with M. Laporta). In “Number Theory for the Millennium, II” (Proceedings of the Millennial Conference on Number Theory, Urbana, IL: May 21–26, 2000), AK Peters, 2002, pp. 307–329.
  8. Squarefree numbers in short intervals. An old unpublished note; see Explicit bounds for large gaps… above for a more recent and much improved version.