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Linear and Multilinear Algebra Volume 70, 2022 - Issue 19
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Research Article

Proof of three conjectures on determinants related to quadratic residues

Darij Grinberga Mathematics Department, Drexel University, Philadelphia, PA, USAView further author information
,
Zhi-Wei Sunb Department of Mathematics, Nanjing University, Nanjing, People's Republic of ChinaCorrespondence[email protected]
View further author information
&
Lilu Zhaoc School of Mathematics, Shandong University, Jinan, People's Republic of ChinaView further author information
Pages 3734-3746 | Received 08 Jul 2020, Accepted 13 Nov 2020, Published online: 02 Dec 2020

References

  • Ireland K, Rosen M. A classical introduction to modern number theory. 2nd ed. New York (NY): Springer; 1990. (Grad Texts Math.; 84).
  • Sun Z-W. On some determinants with Legendre symbol entries. Finite Fields Appl. 2019;56:285–307.
  • Chapman R. Determinants of Legendre symbol matrices. Acta Arith. 2004;115:231–244.
  • Vsemirnov M. On the evaluation of R. Chapman's ‘evil determinant’. Linear Algebra Appl. 2012;436:4101–4106.
  • Vsemirnov M. On R. Chapman's ‘evil determinant’: case p ≡ 1 (mod 4). Acta Arith. 2013;159:331–344.
  • Sun Z-W. Sequence A228379 at OEIS (On-Line Encyclopedia of Integer Sequences). August 21, 2013. Available from: http://oeis.org/A228379
  • Krattenthaler C. Advanced determinant calculus: a complement. Linear Algebra Appl. 2005;411:68–166.
  • Muir T, Metzler WH. A treatise on the theory of determinants. New York (NY): Dover Publ. Inc.; 1960.

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