BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alisa Sedunova (Purdue University) DTSTART:20260715T180000Z DTEND:20260715T182500Z DTSTAMP:20260710T111523Z UID:CANT2026/37 DESCRIPTION:Title: Euler-Kronecker constants of maximal real cyclotomic subfields and Kumme r’s conjecture\nby Alisa Sedunova (Purdue University) as part of Com binatorial and additive number theory seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate Center (4th floor).\n\nAbstract\nTh e Euler–Kronecker constant of a number field $K$ is the ratio of the con stant and the residue of the Laurent series of the Dedekind zeta function at $s = 1$. We study the distribution of the Euler–Kronecker constant $\ \gamma_q^+$ of the maximal real subfield $\\mathbb{Q}(\\zeta_q)^+$ as $q$ ranges over the primes. Further\, we consider the distribution of $\\gamma _q^+ - \\gamma_q$\, with $\\gamma_q$ the Euler–Kronecker constant of $\\ mathbb{Q}(\\zeta_q)$ and show how it is connected with Kummer’s conjectu re\, which predicts the asymptotic growth of the relative class number of $\\mathbb{Q}(\\zeta_q)$. We improve\, for example\, the known results on t he bounds on average for the Kummer ratio and we prove analogous sharp bou nds for $\\gamma_q^+ - \\gamma_q$. The methods employed are partly inspire d by those used by Granville (1990) and Croot and Granville (2002) to inve stigate Kummer’s conjecture\, that predicts the asymptotic growth of the relative class number of prime cyclotomic fields. We substantially improv e the known bounds of Kummer’s ratio under three scenarios: no Siegel ze ro\, presence of Siegel zero and assuming the Riemann Hypothesis for the D irichlet $L$-series attached to odd characters only. \nThe talk is based o n joint papers with A. Languasco\, P. Moree\, N. Kandhil and S. Saad Eddin .\n LOCATION:https://researchseminars.org/talk/CANT2026/37/ END:VEVENT END:VCALENDAR