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Last modified 2 October 2010
Preprints and Expository Notes   

                                           
Papers and Preprints:


20.
Product of simplices and sets of positive upper density in R^d (with Akos Magyar)
          submitted

19.
Simplices and sets of positive upper density in R^d (with Lauren Huckaba and Akos Magyar)
          submitted

18.
Distances in dense subsets of Z^d (with Akos Magyar)
          preprint

17.
Difference sets and polynomials (with Alex Rice)
          submitted

16.
Polynomials and primes in generalized arithmetic progressions (with Ernie Croot and Alex Rice)
          Int. Math. Res. Not. (2015), no. 15, 6021-6043

15.
A quantitative result on Diophantine approximation for intersective polynomials (with Alex Rice)
          INTEGERS Volume 15A (2015), Proceedings of Integers 2013: The Erdös Centennial Conference

14.
A purely combinatorial approach to simultaneous polynomial recurrence modulo 1 (with Ernie Croot and Alex Rice)
Proc. Amer. Math. Soc. 143 (2015), no. 8, 3231-3238

13.
Improved bounds on Sarkozy's theorem for quadratic polynomials (with Mariah Hamel and Alex Rice)
Int. Math. Res. Notices (2013), no. 8, 1761-1782

12.
A new proof of Sarkozy's theorem
Proc. Amer. Math. Soc. 141 (2013), 2253-2264

11.
Polynomial differences in the primes (with Alex Rice)
Combinatorial and Additive Number Theory (Proceedings of CANT 2011 and 2012), pp 129-146. Springer Proc. in Math. & Stat., 2014

10.
Optimal polynomial recurrence (with Akos Magyar)
Canad. J. Math. 65 (2013), no. 1, 171-194
      Here is an exposition of the special case of squares: An optimal version of Sarkozy's theorem

9.
Simultaneous polynomial recurrence (with Akos Magyar)
Bull. Lond. Math. Soc. 43 (2011), no. 4, 765-785

8.
Arithmetic structure in sparse difference sets (with Mariah Hamel, Katherine Thompson and Nathan Walters)
J. Number Theory 130 (2010), 1581-1589

7.
Polynomial configurations in difference sets (with Akos Magyar)
J. Number Theory 129 (2009), 439-450

6.
Strongly singular Radon transforms on the Heisenberg group and folding singularities (with Norberto Laghi)
Proc. Amer. Math. Soc. 136 (2008), no. 4, 1261-1272

5.
Strongly singular integrals along curves (with Norberto Laghi)
Pacific J. Math. 233 (2007), no. 2, 403-415

4.
Strongly singular integral operators associated to different quasi-norms on the Heisenberg group (with Norberto Laghi)
Math. Res. Lett. 14 (2007), no. 5, 825-838
      Here is a related determinant calculation

3.
Two-weight estimates for singular and strongly singular integral operators (with V. Kokilashvili and A. Meskhi)
Acta Math. Hungar. 116 (2007), no.1-2, 1-25

2.
A class of strongly singular Radon transforms on the Heisenberg group
Proc. Edinb. Math. Soc. (2) 50 (2007), 429-457

1.
Strongly singular convolution operators on the Heisenberg group
Trans. Amer. Math. Soc. 359 (2007), 4467-4488



Expository Notes:

  • Two theorems of Sarkozy (with Alex Rice) [This note supersedes the first note in the list below and in addition discusses prime minus one differences]


Some Additional Expository Notes (these are very old, but might still be useful to someone):