Published on *Max-Planck-Institut für Mathematik* (http://www.mpim-bonn.mpg.de)

Posted in

- Vortrag [1]

Speaker:

Armand Noubissie
Zugehörigkeit:

z. Z. MPIM
Datum:

Mit, 22/12/2021 - 14:30 - 15:30 For zoom details contact Pieter Moree (moree@mpim-bonn.mpg.de)

Given an irreducible polynomial f(x) with integer coefficients a rule which for every prime p determines whether f(x) is the product of distinct linear factors is said to be a higher reciprocity law.

In the simplest cases this involves primes being in a union of arithmetic progressions. Beyond that it involves primes being represented by binary quadratic forms or p-th Fourier coefficients of modular forms having a certain value. Here we present such laws involving the value of u_{p-1} modulo p, with u_j the jth term of a highly specific ternary linear recurrence. The methods used to find them

rely on classical algebraic number theory and class field theory. (Joint work in progress with Pieter Moree.)

**Links:**

[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/de/node/246