Related papers: Heuristics on pairing-friendly abelian varieties

We discuss Galois properties of points of prime order on an abelian variety that imply the simplicity of its endomorphism algebra. Applications to hyperelliptic jacobians are given. In particular, we improve some of our earlier results.

In this paper, we give several asymptotic formulas for the number of multiplicatively dependent vectors of algebraic numbers of fixed degree, or within a fixed number field, and bounded height.

We give explicit formulas for the asymptotic Betti numbers, over an arbitrary field, of the ordered configuration spaces of a graph. In characteristic zero, we further give explicit formulas for the asymptotic multiplicities in homology of…

We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the {\em total degree} and the…

We give explicit formulas for the asymptotic Betti numbers of the unordered configuration spaces of an arbitrary finite graph over an arbitrary field.

We introduce the concept of the modularity of an abelian variety defined over the rational number field extending the modularity of an elliptic curve. We discuss the modularity of an abelian variety over the rational number field. We…

In this article we present a heuristic model that describes the asymptotic behaviour of the number of primes p such that the p-th coefficient of a given eigenform is a rational integer. We treat the case of a weight 2 eigenform with…

We give an efficient, deterministic algorithm to decide if two abelian varieties over a number field are isogenous. From this, we derive an algorithm to compute the endomorphism ring of an elliptic curve over a number field.

In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.

In this paper we determine the number of isomorphism classes of superspecial abelian varieties $A$ over the prime field $\Fp$ such that the relative Frobenius morphism $\pi_A$ satisfying $\pi_A^2=-p$.

We study the distribution of algebraic points on curves in abelian varieties over finite fields.

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.

The article motivates, presents and describes large computer calculations concerning the asymptotic behaviour of arithmetic properties of coefficient fields of modular forms. The observations suggest certain patterns, which deserve further…

The paper presents a discussion on the asymptotic formula for the number of plane partitions of a large positive integer.

We prove that for every field k and every positive integer n, there exists an absolutely simple n-dimensional abelian variety over k. We also prove an asymptotic result for finite fields: For every finite field k and positive integer n, we…

We provide a characterization of almost ordinary abelian varieties over finite fields, and use this characterization to provide lower bounds for the sizes of some almost ordinary isogeny classes.

In this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic $p>0$ is isogenous to another one defined over a finite field. We also show that the category of…

If A and B are abelian varieties over a number field K such that there are non-trivial geometric homomorphisms of abelian varieties between reductions of A and B at most primes of K, then there exists a non-trivial (geometric) homomorphism…

We study derived equivalences of Abelian varieties in terms of their associated symplectic data. For simple Abelian varieties over an algebraically closed field of characteristic zero we prove that the natural correspondence introduced by…

Let $a,b>0$ be coprime integers. Assuming a conjecture on Hecke eigenvalues along binary cubic forms, we prove an asymptotic formula for the number of primes of the form $ax^2+by^3$ with $x \leq X^{1/2}$ and $y \leq X^{1/3}$. The proof…