Articles in Press
















  • D. A. Goldston and 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.











  • S. Funkhouser, D. A. Goldston, and A. H. Ledoan, Distribution of Large Gaps Between Primes, Irregularities in the Distribution of Prime Numbers: From the Era of Helmut Maier's Matrix Method sand Beyond (Edited by János Pintz and Michael Th. Rassias), 4567, Springer International Publishing, Switzerland, 2018.
  • A. H. Ledoan, The discrepancy of Farey series, Acta Math. Hungar., (2018), DOI 10.1007/s10474-018-0868-x, 1–16.


Articles Submitted for Publication

  • E. Addison*, A. Ledoan, 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

  • H. A. Ledoan, The level crossings of a random harmonic polynomial, in preparation.
  • H. A. Ledoan, The distribution of complex roots of polynomials with random complex coefficients generated by fractional Brownian motion, in preparation.
  • D. A. Goldston and A. H. Ledoan, On the differences between consecutive prime numbers, II, in preparation.
  • C. Gugg and A. H. Ledoan, 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