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• W3200714565 abstract "For distinct odd primes p and q, we define the Catalan curve C p,q by the affine equation y q =x p -1. In this article we construct the Sato–Tate groups of the Jacobians in order to study the limiting distributions of coefficients of their normalized L-polynomials. Catalan Jacobians are nondegenerate and simple with noncyclic Galois groups (of the endomorphism fields over ℚ), thus making them interesting varieties to study in the context of Sato–Tate groups. We compute both statistical and numerical moments for the limiting distributions. Lastly, we determine the Galois endomorphism types of the Jacobians using both old and new techniques." @default.
• W3200714565 created "2021-09-27" @default.
• W3200714565 creator A5017000204 @default.
• W3200714565 date "2023-05-04" @default.
• W3200714565 modified "2023-10-16" @default.
• W3200714565 title "Sato–Tate Distributions of Catalan Curves" @default.
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• W3200714565 doi "https://doi.org/10.5802/jtnb.1238" @default.
• W3200714565 hasPublicationYear "2023" @default.
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