Section Menu


Articles in Press









  • (with D. A. Goldston) On the differences between consecutive prime numbers, I, INTEGERS: Electronic Journal of Combinatorial Number Theory 12B (2013), #A3, 1–8; reprinted as pp. 37–44 in Combinatorial Number Theory (Proceedings of the ‘‘Integers Conference 2011,’’ Carrollton, Georgia, October 26-29, 2011), De Gruyter Proceedings in Mathematics, 2013.



  • (with K. Crosby, J. Eliseo and D. Mazowiecki) Zeros of partial sums of the square of the Riemann zeta-function, Collaborative Mathematics and Statistics Research, Topics from the 9th Annual UNCG Regional Mathematics and Statistics Conference (Edited by Jan Rychtář, Maya Chhetri, Sat Gupta and Ratnasingham Shivaji), Springer Proc. Math. Statist. 109 (2015), 51-65.

  • (with D. A. Goldston) The jumping champion conjecture, Mathematika 61 (2015), 719-740. (The preprint and published version of the paper are different.)

  • (with D. A. Goldston) Limit points of the sequence of normalized differences between consecutive primes (Dedicated to Prof. Helmut Maier on the occasion of his sixtieth birthday), accepted for publication.


Articles Submitted for Publication

  • The distribution of Farey points in short intervals, submitted for publication.

  • (with K. Ferrier, M. Jackson, D. Patel and H. Tran) The expected number of zeros of a random polynomial, submitted for publication.


Articles in Preparation

  • (with E. Addison, S. Smith and R. Vrandenburgh) Average intensity of the distribution of complex zeros of a class of random polynomials, in preparation.

  • (with D. A. Goldston) On the differences between consecutive prime numbers, II, in preparation.

  • (with S. Starr) The level curves and crossings of a random harmonic polynomial, in preparation.

  • (with C. Gugg) Computations on integers of the form p + gk, in preparation.


Master’s Thesis and Doctoral Dissertation

  • On Turán’s pure power sum problem, Master Theses, Paper 2147 (Adviser: Professor D. A. Goldston), San José State University, San José, CA, May 2001.

  • Distribution of Farey series and free path lengths for a certain billiard in the unit square, Doctoral Dissertation (Adviser: Professor A. Zaharescu), University of Illinois at Urbana-Champaign, Urbana, IL, May 2007. (95 pp.; ISBN: 978-0549-09626-9; ProQuest LLC).


‘It is one of the chief merits of proofs that they instil a certain scepticism as to the result proved.’
          Bertrand Russell, The Principles of Mathematics, 1903, p. 360


‘Here, on the level sand, 
Between the sea and land, 
What shall I build or write 
Against the fall of night? 

Tell me of runes to grave 
That hold the bursting wave, 
Or bastions to design 
For longer date than mine.’
          Alfred Edward Housman, Smooth between sea and land


‘Celui qui multiplie les questions, répondit-elle, augmente ses 
problèmes. Réjouis-toi, mon doux cadavre, de tout ce qui t’est donné, 
et ne pose pas de questions qui ne comportent pas de réponses.’ 
          S. J. Agnon, La Dame et le Colporteur