BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Assif Zaman (University of Toronto) DTSTART:20211110T160000Z DTEND:20211110T170000Z DTSTAMP:20260423T024653Z UID:hnts/42 DESCRIPTION:Title: An approximate form of Artin's holomorphy conjecture and nonvanishing of Art in L-functions\nby Assif Zaman (University of Toronto) as part of Heil bronn number theory seminar\n\n\nAbstract\nLet $k$ be a number field and $ G$ be a finite group\, and let $\\mathfrak{F}_{k}^{G}$ be a family of numb er fields $K$ such that $K/k$ is normal with Galois group isomorphic to $G $. Together with Robert Lemke Oliver and Jesse Thorner\, we prove for many families that for almost all $K \\in \\mathfrak{F}_k^G$\, all of the $L$- functions associated to Artin representations whose kernel does not contai n a fixed normal subgroup are holomorphic and non-vanishing in a wide regi on.\n\nThese results have several arithmetic applications. For example\, w e prove a strong effective prime ideal theorem that holds for almost all f ields in several natural large degree families\, including the family of d egree $n$ $S_n$-extensions for any $n \\geq 2$ and the family of prime deg ree $p$ extensions (with any Galois structure) for any prime $p \\geq 2$. I will discuss this result\, describe the main ideas of the proof\, and sh are some applications to bounds on $\\ell$-torsion subgroups of class grou ps\, to the extremal order of class numbers\, and to the subconvexity prob lem for Dedekind zeta functions.\n LOCATION:https://researchseminars.org/talk/hnts/42/ END:VEVENT END:VCALENDAR