Motivic orthogonal two-dimensional representations of Gal(ℚ/ℚ)

Livné, Ron

doi:10.1007/bf02762074

Cited by 76 publications

(66 citation statements)

References 3 publications

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“…At the same time, we obtain the identification of Q(B(6)) = Q(λ, µ) with Q(s, t) satisfying s 2 = t 3 − 12 3 . This is perhaps slightly more natural than the construction given in [6].…”

Section: It Is Known That γmentioning

confidence: 92%

An interesting elliptic surface over an elliptic curve

Shioda¹,

Schütt²

2007

Proc. Japan Acad. Ser. A Math. Sci.

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Section: It Is Known That γmentioning

confidence: 92%

An interesting elliptic surface over an elliptic curve

Shioda¹,

Schütt²

2007

Proc. Japan Acad. Ser. A Math. Sci.

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“…(11.9) By the moduli theory of K3 surface over C, equality is attained generically in the above rank estimates, but there are countably many specialisations with ρ = 20, the so-called singular K3 surfaces. By a result of Livné [Liv95], singular K3 surfaces over Q are modular. In fact, the associated Hecke eigenform has CM by an imaginary quadratic field of class group exponent two.…”

Section: Picard Numbers By Related Techniquesmentioning

confidence: 99%

Picard numbers of quintic surfaces

Schütt

2014

Proceedings of the London Mathematical Society

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“…On the other hand, M K 5 can be expressed in terms of the p-th eigenvalue for a weight 3 newform on Γ 0 (15) (cf. [14], [17]). M K 6 can be expressed in terms of the p-th eigenvalue for a weight 4 newform on Γ 0 (6) (cf.…”

Section: For Each Nonnegative Integer H By M K(ψ)mentioning

confidence: 99%

INFINITE FAMILIES OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF TERNARY KLOOSTERMAN SUMS WITH SQUARE ARGUMENTS ASSOCIATED WITH O^-(2n, q)

Ким¹

2011

Journal of the Korean Mathematical Society

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Abstract. In this paper, we construct eight infinite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group SO − (2n, q). Here q is a power of three. Then we obtain four infinite families of recursive formulas for power moments of Kloosterman sums with square arguments and four infinite families of recursive formulas for even power moments of those in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of "Gauss sums" for the orthogonal groups O − (2n, q).

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Motivic orthogonal two-dimensional representations of Gal(ℚ/ℚ)

Cited by 76 publications

References 3 publications

An interesting elliptic surface over an elliptic curve

An interesting elliptic surface over an elliptic curve

Picard numbers of quintic surfaces

INFINITE FAMILIES OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF TERNARY KLOOSTERMAN SUMS WITH SQUARE ARGUMENTS ASSOCIATED WITH O^-(2n, q)

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Motivic orthogonal two-dimensional representations of Gal(ℚ/ℚ)

Cited by 76 publications

References 3 publications

An interesting elliptic surface over an elliptic curve

An interesting elliptic surface over an elliptic curve

Picard numbers of quintic surfaces

INFINITE FAMILIES OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF TERNARY KLOOSTERMAN SUMS WITH SQUARE ARGUMENTS ASSOCIATED WITH O-(2n, q)

Contact Info

Product

Resources

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INFINITE FAMILIES OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF TERNARY KLOOSTERMAN SUMS WITH SQUARE ARGUMENTS ASSOCIATED WITH O^-(2n, q)