PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan.

Title:Sums of almost equal squares of primes
Seminar:Algebra and Number Theory Seminar
Speaker:Angel Kumchev, Towson University
Abstract:
We study the representations of large integers $n$ as sums $p_1^2 + \dots + p_s^2$, where $p_1, \dots, p_s$ are primes with $| p_i - (n/s)^{1/2} | \le n^{\theta/2}$, for some fixed $\theta < 1$. When $s = 5$ we use a sieve method to show that all sufficiently large integers $n \equiv 5 \pmod {24}$ can be represented in the above form for $\theta > 8/9$. This improves on earlier work by Liu, L\"{u} and Zhan, who established a similar result for $\theta > 9/10$. We also obtain estimates for the number of integers $n$ satisfying the necessary local conditions but lacking representations of the above form with $s = 3, 4$. When $s = 4$ our estimates improve and generalize recent results by L\"{u} and Zhai, and when $s = 3$ they appear to be first of their kind. This is joint work with Taiyu Li.

Room Reservation Information

Room Number:MB106
Date:01 / 12 / 2012
Time:11:15am - 12:05pm