Abstract
The evaluation of determinants with Legendre symbol entries is a classical topic both in number theory and in linear algebra. Recently Sun posed some conjectures on this topic. In this paper we confirm some of them via Gauss sums and the matrix determinant lemma.
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Acknowledgements
We thank the referee for indispensable suggestions. We also thank Prof. Z.-W. Sun and Prof. H. Pan for their helpful comments.
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This research is supported by the National Natural Science Foundation of China (Grant No. 11971222). The second author is also supported by NUPTSF (Grant No. NY220159).
*Chapman unexpectedly passed away (aged just 57) on October 18, 2020.
Dedicating this paper to the memory of Robin Chapman*
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Wang, L.Y., Wu, H.L. On certain determinants involving Legendre symbols. Ramanujan J 58, 43–56 (2022). https://doi.org/10.1007/s11139-021-00472-1
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DOI: https://doi.org/10.1007/s11139-021-00472-1