Articles in press
- (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 seventy-fifth 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
- (with E. Alkan and A. Zaharescu) On Dirichlet L-functions and the index of visible points, Illinois J. of Math. 51 (2007), No. 2, 455–477.
(with E. Alkan, M. Vajaîtu and A. Zaharescu) On the index of fractions with square-free 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.
(with A. Zaharescu) Real moments of the restrictive factor, Proc. Indian Acad. Sci. (Math. Sci.) 119 (2009), No. 4, 559–566.
(with A. Zaharescu) Square-full divisors of square-full integers, INTEGERS: Electronic Journal of Combinatorial Number Theory 10 (2010), 243–256.
(with S. M. Gonek) Zeros of partial sums of the Riemann zeta-function, Int. Math. Res. Not. 2010, No. 10, 1775–1791.
(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 zeta-function (Dedicated to Prof. Akio Fujii on the occasion of his retirement), Comment. Math. Univ. St. Pauli 60, No. 1, 2 (2011), 171–188.
(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 zeta-function, J. Math. Anal. Appl. 395 (2012), 275–283.
(with D. A. Goldston) On the differences between consecutive prime numbers, I, INTEGERS: Electronic Journal of Combinatorial Number Theory 12B (2013), 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 26-29, 2011), De Gruyter Proceedings in Mathematics, 2013.
(with A. Roy and A. Zaharescu) Zeros of partial sums of the Dedekind zeta function of a cyclotomic field, J. Number Theory 136 (2014), 118-133.
- (with P. Spiegelhalter and A. Zaharescu) Eigenvalues and arithmetic functions on PSL2(Z), accepted for publication in INTEGERS: Electronic Journal of Combinatorial Number Theory.
Articles submitted for publication
(with D. A. Goldston) The jumping champion conjecture, submitted for publication.
(with A. Zaharescu) A divisibility obstruction for certain walks on Gaussian integers, submitted for publication.
On the distribution of Farey points in short intervals, submitted for publication.
(with K. Crosby, J. Eliseo and D. Mazowiecki) Zeros of partial sums of the square of the Riemann zeta-function, submitted for publication.
Articles in preparation
(with D. A. Goldston) Limit points of the sequence of normalized differences between consecutive primes, I, in preparation.
(with D. A. Goldston) On the differences between consecutive prime numbers, II, in preparation.
(with B. Belinskiy and J. V. Matthews) Complex zeros of a random algebraic polynomial with complex coefficients, in preparation.
(with C. Gugg) Computations on integers of the form p + gk, in preparation.
Master’s thesis and 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 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.
‘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