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PreprintCC BY 4.0arXiv

On the Real Waring Rank of a Biharmonic Form

  • Hua-Lin Huang
  • Yiming Liu
  • Yilun Tang
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Abstract

We develop an effective method for determining the real Waring rank and the real border rank of biharmonic binary forms. By means of real apolarity, we convert both of these problems into membership questions for regions bounded by a hypocycloid and an epicycloid. We further provide a computable algebraic criterion for the relevant memberships, which involves only the signs of certain real-valued resultants.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026real,
  title = {{On the Real Waring Rank of a Biharmonic Form}},
  author = {Hua-Lin Huang and Yiming Liu and Yilun Tang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17565},
  eprint = {2610.17565},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17565},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Real Waring Rank of a Biharmonic Form
AU  - Hua-Lin Huang
AU  - Yiming Liu
AU  - Yilun Tang
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17565
UR  - https://arxiv.org/abs/2610.17565
AB  - We develop an effective method for determining the real Waring rank and the real border rank of biharmonic binary forms. By means of real apolarity, we convert both of these problems into membership questions for regions bounded by a hypocycloid and an epicycloid. We further provide a computable algebraic criterion for the relevant memberships, which involves only the signs of certain real-valued resultants.
ER  -