Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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EVEN 2-UNIVERSAL QUADRATIC FORMS OF RANK 5

  • Ji, Yun-Seong (Research Institute of Mathematics Seoul National University) ;
  • Kim, Myeong Jae (Department of Mathematical Sciences Seoul National University) ;
  • Oh, Byeong-Kweon (Department of Mathematical Sciences Seoul National University)
  • Received : 2020.05.21
  • Accepted : 2020.11.23
  • Published : 2021.07.01
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Abstract

A (positive definite integral) quadratic form is called even 2-universal if it represents all even quadratic forms of rank 2. In this article, we prove that there are at most 55 even 2-universal even quadratic forms of rank 5. The proofs of even 2-universalities of some candidates will be given so that exactly 20 candidates remain unproven.

Keywords

Acknowledgement

This work of the first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (NRF-2017R1A5A1015626) and the Ministry of Education (NRF-2019R1I1A1A01060756). This work of the second and the third author was supported by the National Research Foundation of Korea (NRF-2019R1A2C1086347 and NRF-2020R1A5A1016126).

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