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Publikováno v:
Expositiones Mathematicae. 40:1181-1228
We examine the Pythagoras number $\mathcal{P}(\mathcal{O}_K)$ of the ring of integers $\mathcal{O}_K$ in a totally real biquadratic number field $K$. We show that the known upper bound $7$ is attained in a large and natural infinite family of such fi
Publikováno v:
Proceedings of the American Mathematical Society.
We show how to construct discretely ordered principal ideal subrings of Q [ x ] \mathbb {Q}[x] with various types of prime behaviour. Given any set D \mathcal D consisting of finite strictly increasing sequences ( d 1 , d 2 , … , d l ) (d_1,d_2,\do