“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

 

 

Articles in Press

2006

E. Alkan, A.H. Ledoan, M. Vajaîtu, 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, A. Zaharescu,  A parity problem on the free path length of a billiard in the unit square with pockets, Funct. Approx. Comment. Math., 35 (2006), 19-36.

E. Alkan, A.H. Ledoan, M. Vâjâitu, A. Zaharescu, Discrepancy of fractions with divisibility constraints, Monatsh. Math., 149 (2006), No. 3, 265-276.

 

2007

E. Alkan, A.H. Ledoan, A. Zaharescu, On Dirichlet L-functions and the index of visible points, Illinois J. of Math., 51 (2007), No. 2, 455-477.

 

2008

E. Alkan, A.H. Ledoan, M. Vajaîtu, 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.

 

2009

A. Ledoan, A. Zaharescu, Real moments of the restrictive factor, Proc. Indian Acad. Sci. (Math. Sci.), 119 (2009), No. 4, 559-566.

 

2010

A.H. Ledoan, A. Zaharescu, Square-full divisors of square-full integers, Integers, 10 (2010), #A20, 243-256.

A.H. Ledoan, S.M. Gonek, Zeros of partial sums of the Riemann zeta-function, Int. Math. Res. Not., 2010, No. 10, 1775-1791.

 

2011

D.A. Goldston, A.H. Ledoan, Jumping champions and gaps between consecutive primes, Int. J. Number Theory, 7 (2011), No. 6, 1-9.

A. Ledoan, A. Zaharescu, Explicit formulas for the pair correlation of vertical shifts of the zeros of the Riemann zeta-function, Comment. Math. Univ. St. Pauli, 60 (2011), No. 1, 2, 171-188.

 

2012

A. Ledoan, M. Merkli, S. Starr, A universality property of Gaussian analytic functions, J. Theoret. Probab., 25 (2012), No. 2, 496-504.

A. Ledoan, A. Zaharescu, The pair correlation of homotetic images of zeros of the Riemann zeta-function, J. Math. Anal. Appl., 395 (2012), 275-283.

 

2013

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.

 

2014 

A. Ledoan, A. Roy, 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, A. Zaharescu, A divisibility obstruction for certain walks on Gaussian integers, Integers, 14 (2014), #A56, 1-8.

 

2015 

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 (ed. J. Rychtář, M. Chhetri, S. Gupta, R. Shivaji), Springer Proc. Math. Statist., 109 (2015), 51-65.

D.A. Goldston, 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, 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 (ed. C. Pomerance, M. Th. Rassias), Springer Int. Pub., Switzerland, 2015, 115-125.

 

2016

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.

 

2017

K. Ferrier, M. Jackson, A. Ledoan, D. Patel, H. Tran, The expected number of complex zeros of complex random polynomials, Illinois J. of Math., 61 (2017), No. 1-2, 211-224.

 

2018

S. Funkhouser, D.A. Goldston, 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.

 

2020

J.R. Graef, L. Kong, A. Ledoan, M. Wang, Stability analysis of a fractional online social network model, Math. Comput. Simulat., 178 (2020), 625-645.

C. Corley, A. Ledoan, The density of complex zeros of random sums, J. Approx. Theory, 258 (2020), 105461, https://doi.org/10.1016/j.jat.2020.105461.

C. Gugg and A. Ledoan, On the theorem of N. P. Romanoff, Integers, 10 (2020), #A63, 1-15.

  

 

Preprints / 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.

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

C. Corley, A. Ledoan, On the average number of level crossings of random sums, preprint.

 

 

In Preparation

C. Corley, A. Ledoan, On roots of random sums and Brownian motion, in preparation.

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

 

 

Master’s Thesis

Ledoan, Andrew H., On Turán’s pure power sum problem (2001), Master’s Theses, 2147, DOI: https://doi.org/10.31979/etd.h9hg-w7ep.

 

 

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).

 

We dance round in a ring and suppose,
But the Secret sits in the middle and knows.
       Robert Frost

“My mind was struck by a flash of lightning in which its desire was fulfilled.
       Dante, Paradiso, Canto XXXIII