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Binary quadratic forms represented by sums of squares in an essentially unique way

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Abstract

In this article, we determine all positive definite integral binary quadratic forms that are represented by the sum of k integer squares in an essentially unique way for each integer \(k\ge 4\).

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Authors and Affiliations

  1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, 08826, Korea

    Myung-Hwan Kim & Byeong-Kweon Oh

  2. Department of Mathematical Sciences, Seoul National University, Kwanak-ro 1, Kwanak-gu, Seoul, 08826, Korea

    Dayoon Park

Authors
  1. Myung-Hwan Kim
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  2. Byeong-Kweon Oh
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  3. Dayoon Park
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Correspondence to Dayoon Park.

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M.-H. Kim and D. Park were supported by the Institute of Information & Communications Technology Planning & Evaluation grant, funded by the Korean Government, MSIT (IITP-B0717-16-0098). B.-K. Oh was supported by the National Research Foundation of Korea (NRF-2017R1A2B4003758).

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Kim, MH., Oh, BK. & Park, D. Binary quadratic forms represented by sums of squares in an essentially unique way. Ramanujan J 52, 445–458 (2020). https://doi.org/10.1007/s11139-019-00169-6

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  • DOI: https://doi.org/10.1007/s11139-019-00169-6

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