Corpus ID: 214802742

On indefinite and potentially universal quadratic forms over number fields

@article{Xu2020OnIA,
  title={On indefinite and potentially universal quadratic forms over number fields},
  author={Fei Xu and Yang Zhang},
  journal={arXiv: Number Theory},
  year={2020}
}
  • Fei Xu, Yang Zhang
  • Published 2020
  • Mathematics
  • arXiv: Number Theory
  • We prove there are infinitely many classes of integral quadratic forms which represent all integers of the ground field locally but not globally once there is such an integral quadratic form over a number field. Moreover, we show that an integral quadratic form with more than one variables represents all integers of the ground number field over the ring of integers of a finite extension of the ground field if and only if this quadratic form represents $1$ over the ring of integers of a finite… CONTINUE READING