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- W4205280224 abstract "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 y 2 = x 2 p − 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." @default.
- W4205280224 created "2022-01-26" @default.
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- W4205280224 date "2022-05-01" @default.
- W4205280224 modified "2023-10-13" @default.
- W4205280224 title "Sato-Tate distributions of y2 = x − 1 and y2 = x2 − 1" @default.
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- W4205280224 doi "https://doi.org/10.1016/j.jalgebra.2022.01.002" @default.
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