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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
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  • Department of Mathematics

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  • In group "(Maths) Number theory "
  • In group "(Maths) Maths seminar series"
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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

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Frank Adams 1
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Martin Orr

martin.orr@manchester.ac.uk

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