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.