## 11 Citations

### Reciprocal polynomials and curves with many points over a finite field

- Mathematics
- 2021

Let Fq2 be the finite field with q 2 elements. We provide a simple and effective method, using reciprocal polynomials, for the construction of algebraic curves over Fq2 with many rational points. The…

### N T ] 2 0 O ct 2 02 1 RECIPROCAL POLYNOMIALS AND CURVES WITH MANY POINTS OVER A FINITE FIELD

- Mathematics
- 2021

Let Fq2 be the finite field with q 2 elements. We provide a simple and effective method, using reciprocal polynomials, for the construction of algebraic curves over Fq2 with many rational points. The…

### N ov 2 01 8 Poincare polynomial for the moduli space M 0 , n ( C ) and the number of points in M 0 , n ( F q )

- Mathematics
- 2018

Let algebraic quasi-projective variety V be defined over the ring Z, i.e, it can be defined by a system (possibly, empty) of homogeneous polynomial equations and non-equalities with integer…

### A G ] 1 5 A pr 2 01 7 A bootstrap for the number of F q r-rational points on a curve over F q

- Mathematics
- 2018

In this note we present a fast algorithm that finds for any r the number Nr of Fqr rational points on a smooth absolutely irreducible curve C defined over Fq assuming that we know N1, . . . , Ng,…

### Poincar´e Polynomial of the Space M 0 ,n ( C ) and the Number of Points of the Space M 0 ,n ( F q )

- Mathematics
- 2017

— A combinatorial proof that the number of points of the space M 0 ,n ( F q ) satisﬁes the recurrent formula for the Poincar´e polynomials of the space M 0 ,n ( C ) is obtained.

### Parahoric Restriction for GSp(4) and the Inner Cohomology of Siegel Modular Threefolds

- Mathematics
- 2016

For irreducible admissible representations of the group of symplectic similitudes GSp(4,F) of genus two over a p-adic number field F, we obtain the parahoric restriction with respect to an arbitrary…

### On the Classification of Low-Degree Ovoids of Q(4,q)

- MathematicsCombinatorica
- 2022

Ovoids of the non-degenerate quadric Q (4 , q ) of PG(4 , q ) have been studied since the end of the ’80s. They are rare objects and, beside the classical example given by an elliptic quadric, only…

### Cohomology of the Universal Abelian Surface with Applications to Arithmetic Statistics

- Mathematics
- 2020

The moduli stack $\mathcal A_2$ of principally polarized abelian surfaces comes equipped with the universal abelian surface $\pi: \mathcal X_2 \to \mathcal A_2$. The fiber of $\pi$ over a point…

### $\mathbb{F}_{p^2}$-maximal curves with many automorphisms are Galois-covered by the Hermitian curve

- Mathematics
- 2017

Let $\mathbb{F}$ be the finite field of order $q^2$, $q=p^h$ with $p$ prime. It is commonly atribute to J.P. Serre the fact that any curve $\mathbb{F}$-covered by the Hermitian curve…

## References

SHOWING 1-10 OF 55 REFERENCES

### Genus bounds for curves with fixed Frobenius eigenvalues

- Mathematics
- 2013

For every finite collection C of abelian varieties over F_q, we produce an explicit upper bound on the genus of curves over F_q whose Jacobians are isogenous to a product of powers of elements of C.

### Rational Points on Curves Over Finite Fields: Theory and Applications

- Mathematics, Computer Science
- 2001

This chapter discusses function fields with many rational places, applications to algebraic coding theory, and applications to low-discrepancy sequences.

### ON THE NUMBER OF POINTS OF A HYPERELLIPTIC CURVE OVER A FINITE PRIME FIELD

- Mathematics
- 1969

A new method is proposed in this paper for investigating algebraic congruences with prime modulus, leading in the case of hyperelliptic curves to estimates of the same order of strength as the…

### The genus of maximal function fields over finite fields

- Mathematics
- 1995

AbstractWe prove that if there exists a maximal function field of one variable of genusg over
$$\mathbb{F}_{q^2 } $$
, theng≤(q−1)2/4 org=qr/2 withq−1/2≤r≤q−1.

### Tables of curves with many points

- MathematicsMath. Comput.
- 2000

These tables record results on curves with many points over finite fields by giving in two tables the best presently known bounds for N q (g), the maximum number of rational points on a smooth absolutely irreducible projective curve of genus g over a field F q of cardinality q.

### Towers of Function Fields over Non-prime Finite Fields

- Mathematics
- 2012

Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara's…

### Algebraic Stacks Whose Number of Points over Finite Fields is a Polynomial

- Mathematics
- 2005

The aim of this article is to investigate the cohomology (l-adic as well as Betti) of schemes, and more generally of certain algebraic stacks, that are proper and smooth over the integers and have…

### Cohomology of local systems on the moduli of principally polarized abelian surfaces

- Mathematics
- 2015

Let A2 be the moduli stack of principally polarized abelian surfaces. Let V be a smooth ‘-adic sheaf on A2 associated to an irreducible rational finitedimensional representation of Sp.4/. We give an…

### The trace of Hecke operators on the space of classical holomorphic Siegel modular forms of genus two

- Mathematics
- 2009

We prove multiplicity one for vector valued holomorphic Siegel modular forms of weights greater or equal to 3 and the full Siegel modular group and give a trace formula for the action of the Hecke…

### Non-existence of a curve over ₃ of genus 5 with 14 rational points

- Mathematics
- 1999

We show that an absolutely irreducible, smooth, projective curve of genus 5 over F3 with 14 rational points cannot exist.