L-functions at s = 1. IV. First derivatives at s = 0

Special Values of Abelian L - Functions at S = 0

In [12], Stark formulated his far-reaching refined conjecture on the first derivative of abelian (imprimitive) L–functions of order of vanishing r = 1 at s = 0. In [10], Rubin extended Stark’s refined conjecture to describe the r-th derivative of abelian (imprimitive) L-functions of order of vanishing r at s = 0, for arbitrary values r. However, in both Stark’s and Rubin’s setups, the order of ...

Random Matrix Theory and L - Functions at s = 1 / 2

Recent results of Katz and Sarnak [8,9] suggest that the low-lying zeros of families of L-functions display the statistics of the eigenvalues of one of the compact groups of matrices U(N), O(N) or USp(2N). We here explore the link between the value distributions of the L-functions within these families at the central point s = 1/2 and those of the characteristic polynomials Z(U, θ) of matrices ...

Rings of functions with integer derivatives at x=1

0 s Decays at Belle

unique opportunity to study the poorly-known Bs meson. Three analyses, using a sample of 23.6 fb−1, are presented. We report the first observation of the three dominant exclusive Bs decays, Bs → D∗− s π+, Bs → Ds ρ+ and Bs → D∗− s ρ+, the first observation of the CP-eigenstate decay Bs → J/ψ η , and the results from a study of the charmless Bs → K+K−, Bs → K+π−, Bs → π+π− and Bs → K0 S K0 S dec...

Nonvanishing of quadratic Dirichlet L - functions at s

The Generalized Riemann Hypothesis (GRH) states that all non-trivial zeros of Dirichlet L-functions lie on the line Re(s) = 12 . Further, it is believed that there are no Q-linear relations among the non-negative ordinates of these zeros. In particular, it is expected that L( 1 2 , χ) 6= 0 for all primitive characters χ, but this remains still unproved. This appears to have been first conjectur...