BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Winnie Li (Pennsylvania State University) DTSTART:20201027T203000Z DTEND:20201027T213000Z DTSTAMP:20260404T054923Z UID:MITNT/12 DESCRIPTION:Title: P air arithmetical equivalence for quadratic fields\nby Winnie Li (Penns ylvania State University) as part of MIT number theory seminar\n\n\nAbstra ct\nGiven two distinct number fields $K$ and $M$\, and two finite order He cke characters $\\chi$ of $K$ and $\\eta$ of $M$ respectively\, we say tha t the pairs $(\\chi\, K)$ and $(\\eta\, M)$ are arithmetically equivalent if the associated L-functions coincide: $L(s\, \\chi\, K) = L(s\, \\eta\, M)$. When the characters are trivial\, this reduces to the question of fie lds with the same Dedekind zeta function\, investigated by Gassmann in 192 6\, who found such fields of degree 180\, and by Perlis in 1977 and others \, who showed that there are no nonisomorphic fields of degree less than 7 .\n\nIn this talk we discuss arithmetically equivalent pairs where the fie lds are quadratic. They give rise to dihedral automorphic forms induced fr om characters of different quadratic fields. We characterize when a given pair is arithmetically equivalent to another pair\, explicitly construct s uch pairs for infinitely many quadratic extensions with odd class number\, and classify such characters of order 2.\n\nThis is a joint work with Zee v Rudnick.\n LOCATION:https://researchseminars.org/talk/MITNT/12/ END:VEVENT END:VCALENDAR