MathCS Seminar

Title: Spectrum of singularities, exponential sums and the irreducibility of polynomials in two variables
Seminar: Algebra
Speaker: Jorge Jimenez Urroz of U. Politecnica, Catalunya
Contact: John Duncan, john.duncan@emory.edu
Date: 2017-08-29 at 4:00PM
Venue: W306
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Abstract:
In order to control the spectrum of singularities of the generalized Riemann function, we need to find sharp bounds for certain kind of Gauss sums with frequencies on polynomials. This can be achieved by Weil bounds on completely irreducible algebraic curves, which lead us to prove some theorems on irreducibility of polynomials in two variables. We will prove a general theorem in this field. An example of the theorem is the absolute irreducibility of p(x)-p(y)+1, for any p(x) with integer coefficients.

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