We examine the Pythagoras number P (OK) of the ring of integers OK in a totally real
biquadratic number field K. We show that the known upper bound 7 is attained in a large …

We prove that the ring of integers in the totally real cubic subfield K^(49) K (49) of the
cyclotomic field Q (ζ _7) Q (ζ 7) has Pythagoras number equal to 4. This is the smallest …

Sums of squares in function fields of hyperelliptic curves Page 1 Sums of squares in function
fields of hyperelliptic curves Karim Johannes Becher . Jan Van Geel Abstract We study sums of …

It is shown that a valuation of residue characteristic different from 2 and 3 on a field E has at
most one extension to the function field of an elliptic curve over E, for which the residue field …

Given a positive integer n, a sufficient condition on a field is given for bounding its
Pythagoras number by 2 n+ 1. The condition is satisfied for n= 1 by function fields of curves …

This thesis studies quadratic forms and lattices over rings of integers in number fields, and,
to some extent, over non-maximal orders as well. The main focus is on universality of forms …

In this thesis we develop techniques to study sums of squares in fields. We produce methods
to write sums of squares in fields using few squares, and we establish lower bounds for the …

On fields of u-invariant 4 Page 1 Arch. Math. 86 (2006) 31–35 0003–889X/06/010031–05 DOI
10.1007/s00013-005-1491-y © Birkhäuser Verlag, Basel, 2006 Archiv der Mathematik On fields …

Let n∈ N and let K be a field with a henselian discrete valuation of rank n with hereditarily
euclidean residue field. Let F/K be a function field in one variable. It is known that every sum …

For a function field in one variable F/K and a discrete valuation v of K with perfect residue
field k, we bound the number of discrete valuations on F extending v whose residue fields …