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   Emory, Melissa; Goodson, Heidi (May 2022, Journal of Algebra)

   We determine the Sato-Tate groups and prove the generalized Sato-Tate conjecture for the Jacobians of curves of the form y^2 = x^p−1 and y2 = x^{2p}−1, where p is an odd prime. Our results rely on the fact the Jacobians of these curves are nondegenerate, a fact that we prove in the paper. Furthermore, we compute moment statistics associated to the Sato-Tate groups. These moment statistics can be used to verify the equidistribution statement of the generalized Sato-Tate conjecture by comparing them to moment statistics obtained for the traces in the normalized L-polynomials of the curves. 

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   Paul, Srijit; Hanlon, Andrew D.; Hoerz, Ben; Mohler, Daniel; Morningstar, Colin; Wittig, Hartmut (April 2023, 39th International Symposium on Lattice Field Theory)

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