Using the Langlands Program Numberphile video as an excuse to play with Wolfram-Cloud/Mathematica

Published: 19 July 2024
on channel: Thomas Blum

137

In this video we take the Numberphile video on The Langlands Project (featuring Edward Frenkel) as an excuse to play with Wolfram-Cloud/Mathematica. Starting with the elliptic equation y^2 + y = x^3 -x^2 , we write some code to count the number of solution where x, y and the quantities on the left and right-hand sides of the equation are integers modulo some prime p. We collect a list of primes p and the corresponding quantity a(p) which is the prime - the number of solutions for that prime. We then jump over for a "Harmonic" (?) generating function whose coefficients of prime powers match what was found in the previous list. This exercise uses the following Mathematica methods: For, Mod, If, PrimeQ, AppendTo, Product, Series, SeriesCoefficient, ListPlot, Plot, and Show

Watch video Using the Langlands Program Numberphile video as an excuse to play with Wolfram-Cloud/Mathematica online without registration, duration hours minute second in high quality. This video was added by user Thomas Blum 19 July 2024, don't forget to share it with your friends and acquaintances, it has been viewed on our site 137 once and liked it 0 people.