Number Theory Seminar: Lola Thompson
- Date: 04/26/2012
- Time: 15:00
Lecturer(s):
Lola Thompson
Location:
University of British Columbia
Topic:
Products of distinct cyclotomic polynomials
Description:
Abstract
A polynomial is a product of distinct cyclotomic polynomials if and only if it is a divisor over Z[x] of xn–1 for some positive integer n. In this talk, we will examine two natural questions concerning the divisors of xn–1: "For a given n, how large can the coefficients of divisors of xn–1 be?" and "How often does xn–1 have a divisor of every degree between 1 and n?" We will consider the latter question when xn–1 is factored in both Z[x] and Fp[x], using sieve methods and other techniques from analytic number theory in order to obtain our results.
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