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A combinatorial proof of the quadratic Gauss sum
Abstract
We provide an elementary approach to computing the quadratic Gauss sum, emphasizing the method employed to compute the sum corresponding to multiples of 4. The proof method employed does not rely on the law of quadratic reciprocity, but only on exploiting symmetries among the sum's components, together with a recursive approach.
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BibTeX
@misc{campo2026combinatorial,
title = {{A combinatorial proof of the quadratic Gauss sum}},
author = {Adan Medrano Martin del Campo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11075},
eprint = {2610.11075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11075},
}
RIS
TY - UNPB
TI - A combinatorial proof of the quadratic Gauss sum
AU - Adan Medrano Martin del Campo
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.11075
UR - https://arxiv.org/abs/2610.11075
AB - We provide an elementary approach to computing the quadratic Gauss sum, emphasizing the method employed to compute the sum corresponding to multiples of 4. The proof method employed does not rely on the law of quadratic reciprocity, but only on exploiting symmetries among the sum's components, together with a recursive approach.
ER -