Articles in Press
- E. Alkan, A.H. Ledoan, A.M. Vajaîtu, and A. Zaharescu, Discrepancy of sets of fractions with congruence constraints, Rev. Roumaine Math. Pures Appl., 51 (2006), No. 3, 265–276.
- E. Alkan, A.H. Ledoan, and A. Zaharescu, A parity problem on the free path length of a billiard in the unit square with pockets (Dedicated to Prof. Eduard Wirsing on the occasion of his seventy-fifth birthday), Funct. Approx. Comment. Math., 35 (2006), 19–36.
- E. Alkan, A.H. Ledoan, M.M. Vâjâitu, and A. Zaharescu, Discrepancy of fractions with divisibility constraints, Monatsh. Math., 149 (2006), No. 3, 265–276.
E. Alkan, A.H. Ledoan, and A. Zaharescu, On Dirichlet L-functions and the index of visible points, Illinois J. of Math., 51 (2007), No. 2, 455–477.
- E. Alkan, A.H. Ledoan, M. Vajaîtu, and A. Zaharescu, On the index of fractions with square-free denominators in arithmetic progressions, Ramanujan J., 16 (2008), No. 2, 131–161.
- E. Alkan, A.H. Ledoan, A. Zaharescu, Asymptotic behavior of the irrational factor, Acta Math. Hungar. 121 (2008), No. 3, 293–305.
A. Ledoan and A. Zaharescu, Real moments of the restrictive factor, Proc. Indian Acad. Sci. (Math. Sci.), 119 (2009), No. 4, 559–566.
- A.H. Ledoan and A. Zaharescu, Square-full divisors of square-full integers, Integers, 10 (2010), #A20, 243–256.
- A.H. Ledoan and S.M. Gonek, Zeros of partial sums of the Riemann zeta-function, Int. Math. Res. Not., 2010, No. 10, 1775–1791.
- D.A. Goldston and A.H. Ledoan, Jumping champions and gaps between consecutive primes, Int. J. Number Theory, 7 (2011), No. 6, 1–9.
- A. Ledoan and A. Zaharescu, Explicit formulas for the pair correlation of vertical shifts of the zeros of the Riemann zeta-function (Dedicated to Prof. Akio Fujii on the occasion of his retirement), Comment. Math. Univ. St. Pauli, 60 (2011), No. 1, 2, 171–188.
A. Ledoan, M. Merkli, and S. Starr, A universality property of Gaussian analytic functions, J. Theoret. Probab., 25 (2012), No. 2, 496–504.
A. Ledoan and A. Zaharescu, The pair correlation of homotetic images of zeros of the Riemann zeta-function, J. Math. Anal. Appl., 395 (2012), 275–283.
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.
- A. Ledoan, A. Roy, and A. Zaharescu, Zeros of partial sums of the Dedekind zeta function of a cyclotomic field, J. Number Theory, (2012) (2014), 118–133.
- A. Ledoan, P. Spiegelhalter, A. Zaharescu, Eigenvalues and arithmetic functions on PSL2(Z), Integers, 14 (2014), #A14, 1–8.
- A. Ledoan and A. Zaharescu, A divisibility obstruction for certain walks on Gaussian integers, Integers, 14 (2014), #A56, 1–8.
- K. Crosby*, J. Eliseo*, A. Ledoan, and 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), 51–65.
- D.A. Goldston and A.H. Ledoan, The jumping champion conjecture, Mathematika, 61 (2015), Issue 3, 719–740. (The preprint differs from the published version of the paper.)
- D.A. Goldston and A.H. Ledoan, Limit Points of the Sequence of Normalized Differences Between Consecutive Primes, Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday (Edited by Carl Pomerance, Michael Th. Rassias), Springer International Publishing, Switzerland, 2015, 115–125.
A. Ledoan, Explicit formulas for the distribution of complex zeros of a family of random sums, J. Math. Anal. Appl., 444 (2016), Issue 2, 1304–1320.
K. Ferrier*, M. Jackson*, A. Ledoan, D. Patel*, and H. Tran*, The expected number of complex zeros of complex random polynomials, Illinois J. of Math., 61 (2017), No. 1–2, 211–224.
S. Funkhouser, D.A. Goldston, and A.H. Ledoan, Distribution of Large Gaps Between Primes, to appear in Irregularities in the Distribution of Prime Numbers (Edited by János Pintz and Michael Th. Rassias), 2018.
A.H. Ledoan, The discrepancy of Farey series, accepted for publication in Acta Math. Hungar.
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
- 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 represented 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.
On Turán’s pure power sum problem, Master Theses, Paper 2147 (Advisor: D. A. Goldston), San José State University, San José, CA, May 2001.
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 Urbana—Champaign, 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