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 and Beyond (ed. J. Pintz, M. Th. Rassias), 45–67, Springer Int. Pub., Switzerland, 2018.

  • A. H. Ledoan, The discrepancy of Farey series, Acta Math. Hungar., 152 (2018), Issue 2, 465–480.

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.

  • J. R. Graef, L. Kong, A. H. Ledoan, and M. Wang, Stability analysis of a fractional online social network model, submitted for publication.

  • C. Gugg and A. Ledoan, On a theorem of N. P. Romanoff, submitted for publication.

  • E. Eckels, S. Jin, A. Ledoan, and B. Tobin, Linnik’s large sieve and the L1 norm of exponential sums, submitted for publication.

  • C. Corley and A. Ledoan, The density of complex zeros of random sums, submitted for publication.

Articles in Preparation

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

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

  • A. Ledoan, The distribution of complex roots of polynomials with random complex coefficients generated by fractional Brownian motion, in preparation.

Master’s Thesis

Doctoral Dissertation

  • A. H. Ledoan, Distribution of Farey series and free path lengths for a certain billiard in the unit square, Doctoral Dissertation, 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