Abstract
A (positive definite integral) quadratic form is called diagonally 2-universal if it represents all positive definite integral binary diagonal quadratic forms. In this article, we show that, up to equivalence, there are exactly 18 (positive definite integral) quinary diagonal quadratic forms that are diagonally 2-universal. Furthermore, we provide a “diagonally 2-universal criterion” for diagonal quadratic forms, which is similar to “15-Theorem” proved by Conway and Schneeberger.
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This work of the first author was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP)(ASARC, NRF-2007-0056093). This work of the third author was supported by the National Research Foundation of Korea (NRF-2014R1A1A2056296).
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Ji, YS., Kim, M.J. & Oh, BK. Diagonal quadratic forms representing all binary diagonal quadratic forms. Ramanujan J 45, 21–32 (2018). https://doi.org/10.1007/s11139-016-9857-2
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DOI: https://doi.org/10.1007/s11139-016-9857-2