Andrew Ledoan

Visiting Assistant Professor

Department of Mathematics
University of Rochester
Ray P. Hylan Building
Rochester, NY 14627-0138

Office Hours: MW 1530-1730, TTh 1400-1530, and by appointment
Office: 908 Hylan Building
Phone: (585)275-4424
Fax: (585)273-4655
E-mail: ledoan at math dot rochester dot edu

(E-mail is the best way to reach me.)


General Information

I am a visiting assistant professor in the Department of Mathematics at the University of Rochester. I am also a reviewer for Mathematical Reviews and Zentralblatt MATH. I study analysis and number theory, especially sequences, prime numbers, L-functions, and (very recently) Gaussian analytic functions and determinantal point processes. I completed my Ph.D. study in analytic number theory at the University of Illinois at Urbana-Champaign in May 2007, under the direction of Professor A. Zaharescu. In July 2007 I started my postdoctoral appointment at the University of Rochester. The wonderful thing is that I discovered I have a strong interest in probability theory. My postdoctoral advisor is Professor and Chair S. M. Gonek. My postdoctoral appointment will be completed in May 2010. (A few years ago, I spent part of my youth designing GPS algorithms for navigation and timing applications. Memories.)

My Teaching

I love learning and I am dedicated to promoting significant learning experiences among my students. I enjoy solving problems, teaching mathematics on various levels, and helping students. By the end of the 2010 spring term, I will have taught all of the following undergraduate courses at the University of Rochester.

Beyond my postdoctoral appointment, I would love to teach advanced topics courses in analysis and number theory, such as the circle method, sieve methods, and exponential sums. These are my most favorite courses when I was a graduate student.

My Research

I am presently working on several projects involving prime numbers, the general distribution of zeros of the Riemann zeta-function, and random analytic functions. A current list of some of my work follows.

  1. (with C. Gugg) Computations on integers of the form $p+g^k$, work in preparation.
  2. (with S. L. Starr) Local, weak convergence of random analytic functions to a Gaussian limit, work in preparation.
  3. (with A. Zaharescu) On the pair correlation of shifted zeros of the Riemann zeta-function, work in preparation.
  4. (with D. A. Goldston) Prime tuples and gaps between consecutive primes, work in preparation.
  5. (with D. A. Goldston) Jumping champions and gaps between consecutive primes, preprint (available at arXiv.org).
  6. On the distribution of Farey points in short intervals, submitted for publication.
  7. (with A. Zaharescu) Square-full divisors of square-full integers, submitted for publication.
  8. (with S. M. Gonek) Zeros of partial sums of the Riemann zeta-function, accepted for publication in Int. Math. Res. Not.
  9. (with A. Zaharescu) Real moments of the restrictive factor, Proc. Indian Acad. Sci. (Math. Sci.) 119 (2009), no. 4, 559-566.
  10. (with E. Alkan, A. Zaharescu) Asymptotic behavior of the irrational factor, Acta Math. Hungar. 121 (2008), no. 3, 293-305.
  11. (with E. Alkan, M. Vajaitu, A. Zaharescu) On the index of fractions with square-free denominators in arithmetic progressions, The Ramanujan Journal 16 (2008), no. 2, 131-161.
  12. (with E. Akan, A. Zaharescu) On Dirichlet L-functions and the index of visible points, Illinois J. of Math. 51 (2007), no. 2, 455-477.
  13. (with E. Alkan, M. Vajaitu, A. Zaharescu) Discrepancy of sets of fractions with congruence constraints, Rev. Roumaine Math. Pures Appl. 51 (2006), no. 3, 265-276.
  14. (with E. Alkan, A. Zaharescu) A parity problem on the free path length of a billiard in the unit square with pockets, Funct. Approx. Comment. Math. 35 (2006), 19-36.
  15. (with E. Alkan, M. Vajaitu, A. Zaharescu) Discrepancy of fractions with divisibility constraints, Monatsh. Math. 149 (2006), no. 3, 179-192.
  16. Distribution of Farey series and free path lengths for a certain billiard in the unit square, Ph.D. Dissertation, University of Illinois at Urbana-Champaign (Advisor: Professor A. Zaharescu), May 2007.
  17. On Turán’s pure power sum problem, M.S. Thesis, San José State University (Advisor: Professor D. A. Goldston), May 2001.