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. Ferrier, M. Jackson, A. Ledoan, D. Patel, H. Tran, The expected number of complex zeros of complex random polynomials, to appear in Illinois J. of Math. 60 (2017), No. 4.


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


Articles Submitted for Publication

  • A. Ledoan, The discrepancy of Farey points in short intervals, 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, Expected intensity of zeros of random polynomials, 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).


“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