#### Alladi Ramakrishnan Hall

#### The Kummer ratio of the relative class number of prime cyclotomic fields

#### Neelam Kandhil

##### The University of Hong Kong

*A conjecture of Kummer predicts the asymptotic growth of the relative class number of prime cyclotomic fields. The ratio of this class number and the simple asymptotic that Kummer predicted for it, is now called Kummer's ratio. We substantially improve the existing bounds on this ratio in three scenarios: without Siegel zero, with Siegel zero, and assuming the Riemann Hypothesis for the Dirichlet L-series attached to odd characters only. (Joint work with A. Languasco, P. Moree, A. Sedunova, and S. Saad Eddin)*

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