Department of Mathematics Calendar

Back to Listing

The Department of Mathematics Calendar has moved to Webtools. Anyone may submit an event by clicking the "+" button (upper right). Note: the Sponsor field is required. Just type "n/a"

All events will be reviewed before acceptance. Please email Shelby Koehne if you have any questions about submitting an event.

Note: you may search past and future events by clicking on the magnifying glass icon on the main Calendar page.

For an archive of past events: https://math.illinois.edu/research/seminars-department-calendar

Number Theory Seminar: The polynomials X^2+(Y^2+1)^2 and X^2 + (Y^3+Z^3)^2 also capture their primes

Event Type
Seminar/Symposium
Sponsor
n/a
Virtual
wifi event
Date
Feb 22, 2022   11:00 am  
Speaker
Jori Merikoski (Oxford)
Contact
Kevin Ford
E-Mail
ford126@illinois.edu
Views
12
Abstract: We show that there are infinitely many primes of the form X^2+(Y^2+1)^2 and X^2 + (Y^3+Z^3)^2. 
Our work builds on the famous Friedlander-Iwaniec result on primes of the form X^2+Y^4. 
More precisely, Friedlander and Iwaniec obtained an asymptotic formula for the number of primes of this form. 
For the argument we need to estimate Type II sums, which is achieved by an application of the Weil bound, 
both for point-counting and for exponential sums over curves. The type II information we get is too narrow 
for an asymptotic formula, but we can apply Harman's sieve method to establish a lower bound of the 
correct order of magnitude for the number of primes of the form X^2+(Y^2+1)^2 and X^2 + (Y^3+Z^3)^2. 

Zoom: https://illinois.zoom.us/j/84027824197?pwd=TzkyUGRpeDZIcnVxTnpvVEVyLytXUT09

Meeting ID: 840 2782 4197

Password: 271403

link for robots only