The one and only success which it is ours to command is to bring to our work a mighty heart.
       Oliver Wendell Holmes, Jr.

 

Articles in Press

2006

2007

2008

2009

2010

2011

2012

2013

  • (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.

2014

2015

2016

  • Explicit formulas for the distribution of complex zeros of a family of random sums, J. Math. Anal. Appl. (2016), http://dx.doi.org/10.1016/j.jmaa.2016.07.015

 

Articles Submitted for Publication

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

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

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

 

Articles in Preparation

  • Random orthogonal polynomials in the complex plane, in preparation.

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

  • The level crossings of a random harmonic polynomial, in preparation.

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

 

Master’s Thesis

 

Doctoral Dissertation

  • 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