Simpler congruences for Jacobi sum $J(1, 1)_{49}$ of order 49

Ishrat Jahan Ansari; Vikas Jadhav; Devendra Shirolkar

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arXiv · 2510.13924

Simpler congruences for Jacobi sum $J(1, 1)_{49}$ of order 49

Ishrat Jahan Ansari·Vikas Jadhav·Devendra Shirolkar

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Abstract

In this paper we determine the congruence of Jacobi sums $J(1, 1)_{49}$ of order 49 over a field $\mathbb{F}_p$. We also show that simpler congruences hold for $J(1, 1)_{49}$ in the case of artiad and hyperartiad primes.

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Ishrat Jahan Ansari, Vikas Jadhav, Devendra Shirolkar. 2025-10-15. Simpler congruences for Jacobi sum $J(1, 1)_{49}$ of order 49. https://arxiv.org/abs/2510.13924

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