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Articles in Press

2006

2007

2008

2009

2010

2011

2012

2013

2014

  • (with K. Crosby, J. Eliseo and D. Mazowiecki) Zeros of partial sums of the square of the Riemann zeta-function, to appear in Springer Proc. Math. Statist.

  • (with A. Zaharescu) A divisibility obstruction for certain walks on Gaussian integers, to appear in INTEGERS: Electronic Journal of Combinatorial Number Theory.

 

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 + 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

 

‘Celui qui multiplie les questions, répondit-elle, augmente ses 
problèmes. Réjouis-toi, 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

 

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