Cyclic cubic extensions of ℚ

Authors

Dipramit Majumdar, Indian Institute of Technology Madras
B. Sury, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

International Journal of Number Theory

Abstract

We determine the irreducible trinomials X3-aX + b for integers a,b which generate precisely all possible Galois extensions of degree 3 over ℚ. The proof, although involved, is elementary and one can parametrize all these polynomials explicitly. As an accidental by-product of the results, we prove that infinitely many primes congruent to 1 or-1 mod 9 are sums of two rational cubes-thereby, giving the first unconditional result on a classical open problem.

First Page

1929

Last Page

1955

DOI

10.1142/S1793042122500993

Publication Date

10-1-2022

Comments

Open Access, Green

Recommended Citation

Majumdar, Dipramit and Sury, B., "Cyclic cubic extensions of ℚ" (2022). Journal Articles. 2951.
https://digitalcommons.isical.ac.in/journal-articles/2951