A cubic analogue of the Friedlander-Iwaniec spin along primes

Abstract: In 1998 Friedlander and Iwaniec famously proved that there are infinitely many primes of the form a^2+b^4. To show this they defined the spin of Gaussian integers by using the Jacobi symbol, and one of the key ingredients in the proof was to show that the spin becomes equidistributed along Gaussian primes. To generalize this, by using the cubic residue character on the Eisenstein integers, we define the cubic spin of ideals of the twelfth cyclotomic extension. We prove that the cubic spin is equidistributed along prime ideals. The proof of this follows closely along the lines of Friedlander and Iwaniec. We also explain how this cubic spin is related to primes of the form a^2+b^6 on the Eisenstein integers.​

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October