Vanishing of hyperelliptic L-functions at the central point

Non-vanishing of Dirichlet L-functions at the Central Point

On the Nonvanishing of Elliptic Curve L-functions at the Central Point

We show that a large number of elliptic curve L-functions do not vanish at the central point, conditionally on the generalized Riemann hypothesis and on a hypothesis on the regular distribution of the root number. Some hypothesis on the root number is necessary because it has not yet been ruled out that the root number is −1 for almost all elliptic curves. This is the first result of its type f...

Vanishing thetanulls and hyperelliptic curves

Let Mg(2) be the moduli space of curves of genus g with a level-2 structure. We prove that there is always a non hyperelliptic element in the intersection of four thetanull divisors in M6(2). We prove also that for all g > 3, each component of the hyperelliptic locus in Mg(2) is a connected component of the intersection of g−2 thetanull divisors.

Non-vanishing of the Central Derivative of Canonical Hecke L-functions

Every Hecke character of K satisfying (1.1) and (1.2) is actually a quadratic twist of a canonical Hecke character (see Section 2 for a precise description of these characters and which fields have them). Let L(s, χ) denote the Hecke L-function of χ, and Λ(s, χ) its completion; Λ(s, χ) satisfies the functional equation Λ(s, χ) = W (χ)Λ(2 − s, χ), where W (χ) = ±1 is the root number. If χ is a c...

Non - vanishing of the Central Derivative of Canonical Hecke L - functions ( Math

Every Hecke character of K satisfying (1.1) and (1.2) is actually a quadratic twist of a canonical Hecke character (see Section 2 for a precise description of these characters and which fields have them). Let L(s, χ) denote the Hecke L-function of χ, and Λ(s, χ) its completion; Λ(s, χ) satisfies the functional equation Λ(s, χ) = W (χ)Λ(2 − s, χ), where W (χ) = ±1 is the root number. If χ is a c...