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PreprintCC BY 4.0arXiv

A1 - Coulomb branches over finite fields and Selberg Character sums

  • Junzhe Lyu
  • Andrey Smirnov
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Abstract

Motivated by mirror symmetry, we study exponential sums over the š”½q-points of the A1 Coulomb branch. We show that their fiberwise structure is governed by polynomial Gauss sums, providing a geometric realization of Selberg character sums studied by Evans. Using Evans's evaluation, we obtain explicit formulas for the Coulomb-branch exponential sums as products of classical Gauss sums.

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Cite

BibTeXRIS
BibTeX
@misc{lyu2026coulomb,
  title = {{$A_1$ - Coulomb branches over finite fields and Selberg Character sums}},
  author = {Junzhe Lyu and Andrey Smirnov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01443},
  eprint = {2609.01443},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01443},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A_1 - Coulomb branches over finite fields and Selberg Character sums
AU  - Junzhe Lyu
AU  - Andrey Smirnov
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01443
UR  - https://arxiv.org/abs/2609.01443
AB  - Motivated by mirror symmetry, we study exponential sums over the š”½_q-points of the A_1 Coulomb branch. We show that their fiberwise structure is governed by polynomial Gauss sums, providing a geometric realization of Selberg character sums studied by Evans. Using Evans's evaluation, we obtain explicit formulas for the Coulomb-branch exponential sums as products of classical Gauss sums.
ER  -