Graduate Algebra Seminar: Nadir Hajouji

Event Date: 

Thursday, February 16, 2017 - 2:00pm to 3:00pm

Event Location: 

  • 4607B South Hall
Speaker: Nadir Hajouji
Title: The Weil Conjectures & Prescribed Quadratic Residues
While reading* about the Weil conjectures, I came across the following exercise:
Let n be a positive integer, and choose e_1, ..., e_n in the set {1, -1}.  Prove that for all p sufficiently large (relative to n), there exists an integer x such that x+k is a quadratic residue mod p if e_k=1, and x+k is a nonresidue if e_k = -1. 
After giving some background on the Weil conjectures, I will present a solution to the exercise.
*cf., Exercise 7.7