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Description

Number theory seminar II.

Speaker: Anuj Jakhar.

Affiliation: Institute of Mathematical Sciences, Chennai.

Date and Time: Friday 23 August, 4:30 pm - 5:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: On discriminant and integral basis of pure number fields.

Abstract:
By a pure number field we mean an algebraic number field of the type Q(
√n a)
where the polynomial x
n − a with integer coefficients is irreducible over the field
Q of rationals. In this talk our aim is to provide a formula for the discriminant
of pure number fields K = Q(
√n a) where for each prime p dividing n, p does not
divide the gcd of a and vp(a); vp(a) stands for the highest power of p dividing a.
We also describe explicitly an integral basis of such fields. This takes care of all
pure fields K = Q(
√n a), where either a, n are coprime or a is squarefree.

Anuj Jakhar :Institute of Mathematical Sciences, Chennai.