Journal Articles in Number Theory+
- Explicit bounds for large gaps between cubefree integers (with W. McCormick, N. McNew, A. Park, R. Scherr, and W. Ziehr), submitted.
- A framework for discrete bilinear spherical averages and applications to \(\ell^p\)-improving estimates (with T. Anderson and E. Palsson), submitted.
- Short interval results for powerfree polynomials over finite fields (with N. McNew and A. Park), to appear in the International Journal of Number Theory.
- 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.
- Discrete maximal operators for surfaces of higher codimension (with T. Anderson and E. Palsson). (La) Matematica 1 (2022), 442–479.
- On the ergodic Waring-Goldbach problem (with T. Anderson, B. Cook and K. Hughes). Journal of Functional Analysis 282 (2022), Paper 109334, 39 pp.
- 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.
- A hybrid of two theorems of Piatetski-Shapiro (with Zh. Petrov). Monatshefte für Mathematik 189 (2019), 355–376.
- 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.
- On sums of powers of almost equal primes (with H. Liu). Journal of Number Theory 176 (2017), 344–364.
- The strong symmetric genus spectrum of abelian groups (with C. May and J. Zimmerman). Archiv der Mathematik (Basel) 108 (2017), 341–350.
- On the Waring-Goldbach problem for seventh and higher powers (with T. Wooley). Monatshefte für Mathematik 183 (2017), 303–310.
- On the Waring-Goldbach problem for eighth and higher powers (with T. Wooley). Journal of the London Mathematical Society (2) 93 (2016), 811–824.
- On sums of four squares of primes (with L. Zhao). Mathematika 62 (2016), 348–361.
- 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.
- On the convergence of some alternating series. Ramanujan Journal 30 (2013), 101–116.
- Sums of almost equal squares of primes (with T. Li). Journal of Number Theory 132 (2012), 608–636.
- On sums of Ramanujan sums (with T.H. Chan). Acta Arithmetica 152 (2012), 1–10.
- Additive bases arising from functions in a Hardy field (with T.H. Chan and M. Wierdl). Acta Mathematica Hungarica 129 (2010), 263–276.
- On sums of squares of primes II (with G. Harman). Journal of Number Theory 130 (2010), 1969–2002.
- Sums of primes and squares of primes in short intervals (with J. Liu). Monatshefte für Mathematik 157 (2009), 335–363.
- A binary additive equation involving fractional powers. International Journal of Number Theory 5 (2009), 281–292.
- On sums of primes from Beatty sequences. Integers 8 (2008), #A08.
- On the irreducibility of a truncated binomial expansion (with M. Filaseta and D. Pasechnik). Rocky Mountain Journal of Mathematics 37 (2007), 455–464.
- On Weyl sums over primes and almost primes. Michigan Mathematical Journal 54 (2006), 243–268.
- Mean values of Dirichlet polynomials and applications to linear equations with prime variables (with S. Choi). Acta Arithmetica 123 (2006), 125–142.
- On sums of squares of primes (with G. Harman). Mathematical Proceedings of the Cambridge Philosophical Society 140 (2006), 1–13.
- On sums of three squares (with S. Choi and R. Osburn). International Journal of Number Theory 1 (2005), 161–173.
- The Waring–Goldbach problem for seventh powers. Proceedings of the American Mathematical Society 133 (2005), 2927–2937.
- On the Waring–Goldbach problem: Exceptional sets for sums of cubes and higher powers. Canadian Journal of Mathematics 57 (2005), 298–327.
- Quadratic equations with five prime unknowns (with S. Choi). Journal of Number Theory 107 (2004), 357–367.
- 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.
- The difference between consecutive primes in an arithmetic progression. Quarterly Journal of Mathematics Oxford (2) 53 (2002), 479–501.
- Diophantine approximation by cubes of primes and an almost prime II (with J. Brüdern). Illinois Journal of Mathematics 45 (2001), 309–321.
- Diophantine approximation by cubes of primes and an almost prime. Rocky Mountain Journal of Mathematics 30 (2000), 961–980.
- The k-free divisor problem. Monatshefte für Mathematik 129 (2000), 321–327.
- A note on the 2k-th mean value of the Hurwitz zeta-function. Bulletin of the Australian Mathematical Society 60 (1999), 403–405.
- A Diophantine inequality involving prime powers. Acta Arithmetica 89 (1999), 311–330.
- On the distribution of prime numbers of the form \([n^c]\). Glasgow Mathematical Journal 41 (1999), 85–102.
- On an equation with prime numbers (with T. Nedeva). Acta Arithmetica 83 (1998), 117–126.
- On the Piatetski-Shapiro–Vinogradov theorem. Journal de Théorie des Nombres de Bordeaux 9 (1997), 11–23.
- An additive problem with prime numbers from a thin set (with D. Tolev). Acta Mathematica Hungarica 76 (1997), 31–43.
- 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
- 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.
- 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.
- 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.
- 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.
- An invitation to additive prime number theory (with D. Tolev). Serdica Mathematical Journal 31 (2005), 1–74.
- 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.
- Squarefree numbers in short intervals. An old unpublished note; see Explicit bounds for large gaps… above for a more recent and much improved version.