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SUMMARY:Winnie Li
DTSTART:20211011T173000Z
DTEND:20211011T183000Z
DTSTAMP:20260423T053017Z
UID:UNYONTC/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UNYONTC/22/"
 >Pair arithmetical equivalence for quadratic fields</a>\nby Winnie Li as p
 art of Upstate New York Online Number Theory Colloquium\n\n\nAbstract\nGiv
 en two nonisomorphic number fields K and M\, and two finite \norder Hecke 
 characters $\\chi$ of K and $\\eta$ of M respectively\, we say \nthat the 
 pairs $(\\chi\, K)$ and $(\\eta\, M)$ are arithmetically equivalent \nif t
 he associated L-functions coincide: $L(s\, \\chi\, K) = L(s\, \\eta\, M)$.
  \nWhen the characters are trivial\, this reduces to the question of field
 s \nwith the same Dedekind zeta function\, investigated by Gassmann in 192
 6\, \nwho found such fields of degree 180\, and by Perlis in 1977 and othe
 rs\, \nwho showed that there are no arithmetically equivalent fields of de
 gree \nless than 7.\n\nIn this talk we discuss arithmetically equivalent p
 airs where the fields \nare quadratic. They give rise to dihedral automorp
 hic forms induced from \ncharacters of different quadratic fields. We char
 acterize when a given \npair is arithmetically equivalent to another pair\
 , explicitly construct \nsuch pairs for infinitely many quadratic extensio
 ns with odd class \nnumber\, and classify such characters of order 2.\n\nT
 his is a joint work with Zeev Rudnick.\n
LOCATION:https://researchseminars.org/talk/UNYONTC/22/
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