Number Fields
Supervised by Ramesh Sreekantan (Indian Statistical Institute, Bangalore), 2016
Work done during summer 2016 (June 01, 2016 to July 31, 2016). Supported by INSPIRE SHE.
Calculations of the ring of integers, prime ideal factorization and fundamental units for the quadratic, cubic, biquadratic and cyclotomic number fields were performed following the exercises from Marcus’ book “Number Fields”. Kummer’s proof of the first case of Fermat’s Last Theorem, and the proof of Delaunay-Nagell theorem for the number of integer solutions of $x^3+dy^3=1$ were also studied.