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SUMMARY:Ha Tran (Concordia University of Edmonton)
DTSTART:20231128T210000Z
DTEND:20231128T220000Z
DTSTAMP:20260423T021130Z
UID:NTC/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTC/35/">The
  Size Function For Imaginary Cyclic Sextic Fields</a>\nby Ha Tran (Concord
 ia University of Edmonton) as part of Lethbridge number theory and combina
 torics seminar\n\nLecture held in University of Lethbridge: M1060 (Markin 
 Hall).\n\nAbstract\nThe size function $h^0$ for a number field is analogou
 s to the dimension of the\nRiemann-Roch spaces of divisors on an algebraic
  curve. Van der Geer and Schoof conjectured\nthat $h^0$ attains its maximu
 m at the trivial class of Arakelov divisors if that field is Galois over\n
 $\\mathbb{Q}$ or over an imaginary quadratic field. This conjecture was pr
 oved for all number fields with the unit group of rank $0$ and $1$\, and a
 lso for cyclic cubic fields which have unit group of rank\ntwo. In this ta
 lk\, we will discuss the main idea to prove that the conjecture also holds
  for\ntotally imaginary cyclic sextic fields\, another class of number fie
 lds with unit group of rank\ntwo. This is joint work with Peng Tian and Am
 y Feaver.\n
LOCATION:https://researchseminars.org/talk/NTC/35/
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