Higher reciprocity laws and ternary linear recurrences

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.)