“The one and only success which it is ours to command is to bring to our work a mighty heart.”
Oliver Wendell Holmes, Jr.
Articles in Press
2006

(with E. Alkan, M. Vajaîtu and A. Zaharescu) Discrepancy of sets of fractions with congruence constraints, Rev. Roumaine Math. Pures Appl. 51 (2006), No. 3, 265–276.

(with E. Alkan 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 seventyfifth birthday), Funct. Approx. Comment. Math. 35 (2006), 19–36.

(with E. Alkan, M. Vajaîtu and A. Zaharescu) Discrepancy of fractions with divisibility constraints, Monatsh. Math. 149 (2006), No. 3, 265–276.
2007

(with E. Alkan and A. Zaharescu) On Dirichlet Lfunctions and the index of visible points, Illinois J. of Math. 51 (2007), No. 2, 455–477.
2008

(with E. Alkan, M. Vajaîtu and A. Zaharescu) On the index of fractions with squarefree denominators in arithmetic progressions, The Ramanujan Journal 16 (2008), No. 2, 131–161.

(with E. Alkan and A. Zaharescu) Asymptotic behavior of the irrational factor, Acta Math. Hungar. 121 (2008), No. 3, 293–305.
2009

(with A. Zaharescu) Real moments of the restrictive factor, Proc. Indian Acad. Sci. (Math. Sci.) 119 (2009), No. 4, 559–566.
2010

(with A. Zaharescu) Squarefull divisors of squarefull integers, INTEGERS: Electronic Journal of Combinatorial Number Theory 10 (2010), #A20, 243–256.

(with S. M. Gonek) Zeros of partial sums of the Riemann zetafunction, Int. Math. Res. Not. 2010, No. 10, 1775–1791.
2011

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

(with A. Zaharescu) Explicit formulas for the pair correlation of zeros of the Riemann zetafunction (Dedicated to Prof. Akio Fujii on the occasion of his retirement), Comment. Math. Univ. St. Pauli 60, No. 1, 2 (2011), 171–188.
2012

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

(with A. Zaharescu) The pair correlation of homotetic images of zeros of the Riemann zetafunction, J. Math. Anal. Appl. 395 (2012), 275–283.
2013

(with D. A. Goldston) On the differences between consecutive prime numbers, I, INTEGERS: Electronic Journal of Combinatorial Number Theory 12B (2013), #A3, 1–8; reprinted as pp. 37–44 in Combinatorial Number Theory (Proceedings of the ‘‘Integers Conference 2011,’’ Carrollton, Georgia, October 2629, 2011), De Gruyter Proceedings in Mathematics, 2013.
2014

(with A. Roy and A. Zaharescu) Zeros of partial sums of the Dedekind zeta function of a cyclotomic field, J. Number Theory 136 (2014), 118133.

(with P. Spiegelhalter and A. Zaharescu) Eigenvalues and arithmetic functions on PSL_{2}(Z), INTEGERS: Electronic Journal of Combinatorial Number Theory 14 (2014), #A14, 1–8.

(with A. Zaharescu) A divisibility obstruction for certain walks on Gaussian integers, INTEGERS: Electronic Journal of Combinatorial Number Theory 14 (2014), #A56, 1–8.
2015

(with K. Crosby, J. Eliseo and D. Mazowiecki) Zeros of partial sums of the square of the Riemann zetafunction, Collaborative Mathematics and Statistics Research, Topics from the 9th Annual UNCG Regional Mathematics and Statistics Conference (Edited by Jan Rychtář, Maya Chhetri, Sat Gupta and Ratnasingham Shivaji), Springer Proc. Math. Statist. 109 (2015), 51–65.

(with D. A. Goldston) The jumping champion conjecture, Mathematika 61 (2015), Issue 3, 719–740. (The preprint differs from the published version of the paper.)

(with D. A. Goldston) 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 and Michael Th. Rassias), Springer International Publishing, Switzerland, 2015, 115–125.
2016

Explicit formulas for the distribution of complex zeros of a family of random sums, J. Math. Anal. Appl. (2016), http://dx.doi.org/10.1016/j.jmaa.2016.07.015
Articles Submitted for Publication

The discrepancy of Farey points in short intervals, submitted for publication.

(with K. Ferrier, M. Jackson, D. Patel and H. Tran) The expected number of complex zeros of a random polynomial, submitted for publication.

(with E. Addison, 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

Random orthogonal polynomials in the complex plane, in preparation.

(with D. A. Goldston) On the differences between consecutive prime numbers, II, in preparation.

The level crossings of a random harmonic polynomial, in preparation.

(with C. Gugg) Computations on integers of the form p + g^{k}, preprint.
Master’s Thesis

On Turán’s pure power sum problem, Master Theses, Paper 2147 (Adviser: Professor D. A. Goldston), San José State University, San José, CA, May 2001.
Doctoral Dissertation

Distribution of Farey series and free path lengths for a certain billiard in the unit square, Doctoral Dissertation (Adviser: Professor A. Zaharescu), University of Illinois at UrbanaChampaign, Urbana, IL, May 2007. (95 pp.; ISBN: 9780549096269; 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