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SUMMARY:Daniel Gil Muñoz (Charles University in Prague)
DTSTART:20211006T100000Z
DTEND:20211006T110000Z
DTSTAMP:20260423T021528Z
UID:SIMBa/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIMBa/13/">O
 n the possible ranks of universal quadratic forms over totally real number
  fields</a>\nby Daniel Gil Muñoz (Charles University in Prague) as part o
 f Barcelona Mathematics Informal Seminar (SIMBa)\n\n\nAbstract\nA quadrati
 c form $Q(X_1\,...\,X_n)$ over the integer numbers is said to be universal
  if it represents all positive integers\, that is\, for every $a \\in \\ma
 thbb{Z}>0$ there is a vector $(\\alpha_1\,...\,\\alpha_n)\\in \\mathbb{Z}^
 n$ such that $Q(\\alpha_1\,...\,\\alpha_n) = a$. The topic of universal qu
 adratic forms is quite classical in arithmetic\; for instance\, Lagrange's
  1770 four square theorem asserts that the sum of four squares is a univer
 sal quadratic form over $\\mathbb{Z}$. \nIn this talk\, we consider the su
 itable generalization of universality for quadratic forms over the number 
 ring $\\mathcal{O}_K$ of a totally real number field $K$ and view some rec
 ent results on the possible ranks (number of variables $X_i$) of universal
  quadratic forms over different families of totally real number\nfields.\n
LOCATION:https://researchseminars.org/talk/SIMBa/13/
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