Pythagoras numbers of orders in biquadratic fields

On Kitaoka's conjecture and lifting problem for universal quadratic forms

“…This leads to the Pythagoras number, a constant well‐studied also in other settings (see, for example, [23]). Yet, in the case of the ring of integers of a totally real number field, all that is known in general is that the Pythagoras number is finite [28] and bounded by the degree of the field [16], but can grow arbitrarily large [28] (in the non‐totally real case, the Pythagoras number $$\leqslant 5$$ [27]; for some small degree cases see [22, 26, 31]). Furthermore, Siegel [29] proved that for each number field $$F$$ there exists $$m\in \mathbb {N}$$ such that all totally positive integers divisible by $$m$$ can be represented as the sum of squares.…”