Sums of squares in function fields over Henselian local fields

Olivier Benoist

doi:10.1007/s00208-019-01935-z

Sums of squares in function fields over Henselian local fields

Algebraic Geometry 2020-10-20 v2 Number Theory

Authors: Olivier Benoist

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Abstract

We give upper bounds for the level and the Pythagoras number of function fields over fraction fields of integral Henselian excellent local rings. In particular, we show that the Pythagoras number of $\mathbb{R}((x_1,\dots,x_n))$ is $\leq 2^{n-1}$ , which answers positively a question of Choi, Dai, Lam and Reznick.

Keywords

multiplicative functions divisor function

Cite

@article{arxiv.1905.11665,
  title  = {Sums of squares in function fields over Henselian local fields},
  author = {Olivier Benoist},
  journal= {arXiv preprint arXiv:1905.11665},
  year   = {2020}
}

Comments

9 pages, minor revision

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