#### Alladi Ramakrishnan Hall

#### On existence of Euclidean ideal classes in certain number fields

#### Jyothsnaa S.

##### IMSc

*In 1979, Lenstra introduced the notion of Euclidean ideal classes*

for Dedekind domains to identify number fields having cyclic class groups. He showed

that under Extended Riemann Hypothesis, class group

of a number field with infinite unit group is cyclic if and only if it has

a Euclidean ideal class.

In this talk, we introduce the relevant notions, indicate the circle of ideas around

this theme and finally discuss some new unconditional results.

Proof of these results involve analytic

and arithmetic tools from class field theory and sieve methods.

Done