Articles in Press















  • D.A. Goldston, A.H. Ledoan, On the differences between consecutive prime numbers, I, Integers 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.







  • K. Crosby*, J. Eliseo*, A. Ledoan, 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, Ratnasingham Shivaji), Springer Proc. Math. Statist. 109 (2015), 5165.


  • D.A. Goldston, A.H. Ledoan, The jumping champion conjecture, Mathematika 61 (2015), Issue 3, 719740. (The preprint differs from the published version of the paper.)








  • S. Funkhouser, D.A. Goldston, A.H. Ledoan, Distribution of Large Gaps Between Primes, accepted for publication in Irregularities in the Distribution of Prime Numbers (Edited by János Pintz and Michael Th. Rassias).


Articles Submitted for Publication

  • A. Ledoan, The discrepancy of Farey series, submitted for publication.

  • E. Addison*, A. Ledoan, S. Smith*, R. Vrandenburgh*, Average intensity of the distribution of complex zeros of a class of random polynomials, submitted for publication.


Articles in Preparation

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

  • D.A. Goldston, A.H. Ledoan, On the differences between consecutive prime numbers, II, in preparation.

  • A.H. Ledoan, 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 (Advisor: A. Zaharescu), University of Illinois at UrbanaChampaign, Urbana, IL, May 2007. (95 pp.; ISBN: 978-0549-09626-9; ProQuest LLC).


An asterisk (*) is used to denote undergraduate co-authors.


“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