## 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. www-math.mit.edu/~poonen/papers/Qpoints.pdf, Exercise 7.7

January 6, 2020 - 11:07am