#### IMSc Webinar

#### Covering the ray class group with a product of prime ideals

#### Jyothsnaa Sivaraman

##### University of Toronto, Canada

*Xylouris's theorem states that given a positive integer $q$, in every invertible residue class modulo $q$ one can find a prime less than $q^{5}$, for $q$ large enough. A broad generalisation of this problem pertains to finding the prime ideal in a number field, of the smallest norm, with a given Artin symbol*

with respect to a chosen Galois extension of the number field. In 2018, Ramar{\'e} and Walker published a paper where they computed a precise bound on $q$ provided one were to allow a product of $3$ primes in place of a single prime in each invertible residue class. In this paper, we would like to adapt the same method to the setup of ray class fields and compare the bounds obtained with known bounds in case of prime ideals.

Google meet link for this talk is

meet.google.com/rez-wwzt-vbe

Done