Statistics for biquadratic covers of the projective line over finite fields

Lorenzo, Elisa; Meleleo, Giulio; Milione, Piermarco; Bucur, Alina

doi:10.48550/arxiv.1503.03276

Cited by 2 publications

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“…Bucur, David, Feigon and Lalin [2], [3] then extended this to prime cyclic curves (G = Z/QZ, Q a prime). Lorenzo, Meleleo and Milione [9] then proved this for n-quadratic curves (G = (Z/2Z) n ). The author [10], [11] completes this for any abelian group.…”

Section: Introductionmentioning

confidence: 84%

Number of Points on the Full Moduli Space of Curves over Finite Fields

Meisner¹

2016

Preprint

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The distribution of the number of points on abelian covers of P 1 (Fq) ranging over an irreducible moduli space has been answered in a recent work by the author [10], [11]. The authors of [1] determined the distribution over the whole moduli space for curves with Gal(K(C)/K) a prime cyclic. In this paper, we prove a result towards determining the distribution over the whole moduli space of curves with Gal(K(C)/K) any abelian group. We successfully determine the distribution in the case Gal(K(C)/K) is a power of a prime cyclic.

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Section: Introductionmentioning

confidence: 84%

Number of Points on the Full Moduli Space of Curves over Finite Fields

Meisner¹

2016

Preprint

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“…First we need two lemmas from other papers. The first one is Lemma 6.4 from [5] saying Lemma 3.1 (Lemma 6.4 from [5]). Let d 1 , .…”

Section: Set Countmentioning

confidence: 99%

“…Hyperelliptic curves are in one-to-one correspondence with Galois extensions of F q (X) with Galois group Z/2Z. Bucur, David, Feigon and Lalin [1], [2] extended this result to smooth projective curves that are in one-to-one correspondence with Galois extensions of F q (X) with Galois group Z/pZ, where p is a prime such that q ≡ 1 mod p. Recently Lorenzo, Milione and Meleleo [5] determined the case for Galois group (Z/2Z) n . In this paper we determine the case for cyclic Galois groups Z/rZ for any q ≡ 1 mod r where r is not necessarily a prime.…”

Section: Introductionmentioning

confidence: 99%

Distribution of points on cyclic curves over finite fields

Meisner

2017

Journal of Number Theory

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We determine in this paper the distribution of the number of points on the cyclic covers of P 1 (Fq) with affine models C :and r th -power free when q is fixed and the genus, g, tends to infinity. This generalize the work of Kurlberg and Rudnick and Bucur, David, Feigon and Lalin who considered different families of curves over Fq. In all cases, the distribution is given by a sum of random variables.

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Statistics for biquadratic covers of the projective line over finite fields

Cited by 2 publications

References 0 publications

Number of Points on the Full Moduli Space of Curves over Finite Fields

Number of Points on the Full Moduli Space of Curves over Finite Fields

Distribution of points on cyclic curves over finite fields

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