Dissertation

# On the computation of norm residue symbols

An algorithm is discussed to compute the exponential representation of principal units in a finite extension field F of the p-adic rationals.

- Author
- Bouw, J.
- Date
- 19 May 2021
- Links
- Thesis in Leiden Repository

An algorithm is discussed to compute the exponential representation of principal units in a finite extension field F of the p-adic rationals. Also is discussed the computation of roots of unity contained in F and a special kind of principal unit, which is called a distinguished unit. The properties of norm residue symbols are given and also an algorithm to compute the norm residue symbol. Moreover a strongly distinguished unit is defined and an algorithm is given to compute such a unit. All the algorithms are polynomial time algorithms.