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Articles in press

2006

 

2007

2008

2009

2010

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 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.

2012

2013

 

2014

  • (with A. Roy and A. Zaharescu) Zeros of partial sums of the Dedekind zeta function of a cyclotomic fieldJ. 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 J. V. Matthews) On the complex zeros of a random algebraic polynomial, in preparation.

  • (with C. Gugg) Computations on integers of the form p + gk, 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 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

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