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Sums of values represented by a quadratic form

Berhuy, G ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1007/s00229-012-0551-4
  3. Publisher: 2013
  4. Abstract:
  5. Let q be a quadratic form over a field K of characteristic different from 2. We investigate the properties of the smallest positive integer n such that -1 is a sum of n values represented by q in several situations. We relate this invariant (which is called the q-level of K) to other invariants of K such as the level, the u-invariant and the Pythagoras number of K. The problem of determining the numbers which can be realized as a q-level for particular q or K is studied. We also observe that the q-level naturally emerges when one tries to obtain a lower bound for the index of the subgroup of non-zero values represented by a Pfister form q. We highlight necessary and/or sufficient conditions for the q-level to be finite. Throughout the paper, special emphasis is given to the case where q is a Pfister form
  6. Keywords:
  8. Source: Manuscripta Mathematica ; Volume 140, Issue 3-4 , March , 2013 , Pages 531-556 ; 00252611 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00229-012-0551-4