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Higher reciprocity laws and ternary linear recurrences

Posted in
Armand Noubissie
z. Z. MPIM
Wed, 22/12/2021 - 14:30 - 15:30
Parent event: 
Number theory lunch seminar

For zoom details contact Pieter Moree (


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.)


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