Sato–Tate distributions of twists ofy2=x5−xandy2=x6+ 1

Fité, Francesc; Sutherland, Andrew V.

doi:10.2140/ant.2014.8.543

Cited by 30 publications

(39 citation statements)

References 14 publications

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“…Closed formulas for these sequences are determined in §2 in the more general setting of abelian threefolds defined over a number field k that are Qisogenous to the cube of an elliptic curve defined over k; see Proposition 2.2 and Corollary 2.4. This analysis closely follows the techniques developed in [FS14,§3].…”

Section: Introductionmentioning

confidence: 91%

Sato–Tate distributions of twists of the Fermat and the Klein quartics

2018

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We determine the limiting distribution of the normalized Euler factors of an abelian threefold A defined over a number field k when A is Q-isogenous to the cube of a CM elliptic curve defined over k. As an application, we classify the Sato-Tate distributions of the Jacobians of twists of the Fermat and Klein quartics, obtaining 54 and 23, respectively, and 60 in total. We encounter a new phenomenon not visible in dimensions 1 or 2: the limiting distribution of the normalized Euler factors is not determined by the limiting distributions of their coefficients.

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Section: Introductionmentioning

confidence: 91%

Sato–Tate distributions of twists of the Fermat and the Klein quartics

2018

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“…for every prime p coprime to M. The lemma then follows from Proposition 3.6 of [FS12], which asserts that the x p 's are equidistributed on U(1), even when p is subject to the condition that Frob p = c for some fixed conjugacy class c of Gal(K M /K).…”

Section: Direct Sums Of Correlated Newformsmentioning

confidence: 94%

Sato-Tate groups of some weight 3 motives

Kedlaya¹,

Sutherland²

2016

Contemporary Mathematics

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Abstract. We establish the group-theoretic classification of Sato-Tate groups of self-dual motives of weight 3 with rational coefficients and Hodge numbers h 3,0 = h 2,1 = h 1,2 = h 0,3 = 1. We then describe families of motives that realize some of these Sato-Tate groups, and provide numerical evidence supporting equidistribution. One of these families arises in the middle cohomology of certain Calabi-Yau threefolds appearing in the Dwork quintic pencil; for motives in this family, our evidence suggests that the Sato-Tate group is always equal to the full unitary symplectic group USp(4).

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“…Before we proceed to prove the theorem, we first recall some basic facts concerning newforms with complex multiplication, following the exposition given in [7, Section 2, pp. [8][9].…”

Section: Preliminariesmentioning

confidence: 99%