Computation of Jacobi sums of order l^2 and 2l^2 with prime l
This work addresses a computational bottleneck in number theory for researchers dealing with Jacobi sums, but it is incremental as it builds on existing methods for specific orders.
The paper tackled the problem of efficiently computing Jacobi sums of orders l^2 and 2l^2 for odd prime l by developing fast algorithms that express these sums using the minimal number of cyclotomic numbers, and it implemented validation algorithms to confirm the minimality of the cyclotomic numbers used.
In this paper, we present the fast computational algorithms for the Jacobi sums of orders $l^2$ and $2l^{2}$ with odd prime $l$ by formulating them in terms of the minimum number of cyclotomic numbers of the corresponding orders. We also implement two additional algorithms to validate these formulae, which are also useful for the demonstration of the minimality of cyclotomic numbers required.