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 |