Manchester Number Theory Seminar - Pedro Cazorla Garcia
| Dates: | 8 November 2022 |
|---|
| Times: | 15:00 - 16:00 |
|---|
| What is it: | Seminar |
|---|
| Organiser: | Department of Mathematics |
|---|
| Who is it for: | University staff, External researchers, Current University students |
|---|
|
Speaker: Pedro Cazorla Garcia (University of Manchester)
Title: The generalised Lebesgue-Ramanujan-Nagell equation
Abstract: The Lebesgue-Ramanujan-Nagell equation x^2 + D = y^n has been studied extensively by number theorists during the last century, both by its intrinsic interest and as a generalisation to Catalan's conjecture. With the advent of the modular methodology developed by Wiles, Ribet and others and employed in the proof of Fermat's last theorem, along with the evolution of computational number theory techniques, it is now feasible to consider the generalised Lebesgue-Ramanujan-Nagell equation C1x^2 + C2 = y^n.
In this talk, we will discuss a variety of techniques which allow us to solve the aforementioned equation in the range 1 <= C1, C2 <= 20, involving the modularity of Galois representations and Thue equations. All of this is joint work with Vandita Patel.
Room: Frank Adams 1
Travel and Contact Information
Find event
Frank Adams 1
Alan Turing Building
Manchester
