Master's Project Defense: Representations of sums of three squares along arithmetic progressions | Department of Mathematics

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Master's Project Defense: Representations of sums of three squares along arithmetic progressions

Event Information
Event Location: 
GAB 461
Event Date: 
Wednesday, March 4, 2020 - 2:30pm

Professor Richter invites you to attend the Master's project defense of Ethan Malmer.

Title: "Representations of sums of three squares along arithmetic progressions"

Abstract:
For a positive integers n, set r(n):=#{(x,y,x) in Z3 : x2+y2+z2=n}. Let g be a positive integer, and A mod M be a congruence class containing a squarefree integer. In this talk, we present a result of Pollack, which asserts that there are infinitely many squarefree positive integersn≡A mod M for which g divides r(n). For the proof we recall some properties and results of class groups and class numbers of imaginary quadratic fields. We show that there are infinitely many positive squarefree integers d≡A mod M for which the class group of Q(sqrt{-d}) contains an element of order g, which then implies Pollack's result.

Cookies and coffee will be served in GAB 472 following the event.

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