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. L. 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.

(with D. A. Goldston) On the differences between consecutive prime numbers, I, 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 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), 5165.

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

(with D. A. Goldston) The jumping champion conjecture, submitted for publication.

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

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

(with D. A. Goldston) Limit points of the sequence of normalized differences between consecutive primes, preprint.

(with A. Roy and A. Zaharescu), Mathematical billiards, in preparation.

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

(with J. V. Matthews) Value distribution of a complex Gaussian random polynomial, in preparation.

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

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.

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.
‘Here, on the level sand,
Between the sea and land,
What shall I build or write
Against the fall of night?
Tell me of runes to grave
That hold the bursting wave,
Or bastions to design
For longer date than mine.’
Alfred Edward Housman, Smooth between sea and land
‘Celui qui multiplie les questions, réponditelle, augmente ses
problèmes. Réjouistoi, mon doux cadavre, de tout ce qui t’est donné,
et ne pose pas de questions qui ne comportent pas de réponses.’
S. J. Agnon, La Dame et le Colporteur