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SUMMARY:Robert Hough (Stony Brook University)
DTSTART:20250523T180000Z
DTEND:20250523T182500Z
DTSTAMP:20260423T041654Z
UID:CANT2025/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/54/
 ">Lower order terms in the shape of cubic fields</a>\nby Robert Hough (Sto
 ny Brook University) as part of Combinatorial and additive number theory (
 CANT 2025)\n\nLecture held in CUNY Graduate Center - Science Center (4th f
 loor).\n\nAbstract\nThe ring of integers of a degree n number field may be
  viewed as an n-dimensional lattice within the canonical embedding.  Spect
 rally expanding the space of lattices\, we study the distribution of latti
 ce shapes of rings of integers when cubic fields are ordered by discrimina
 nt by studying the Weyl sums testing the lattice shape against the real an
 alytic Eisenstein series and Maass cusp forms.  In the case of Eisenstein 
 series we identify a lower order main term of order $X^{11/12}$ when field
 s of discriminant of order $X$ are counted with a smooth weight.  \\\\\nJo
 int work with Eun Hye Lee.  Recent work of Lee and Ramin Tagloo-Bighash pr
 omises to extend these ideas to integral orbits in general prehomogeneous 
 vector spaces.\n
LOCATION:https://researchseminars.org/talk/CANT2025/54/
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