A slow-growing sequence defined by an unusual recurrence.
Automorphic distributions are distributions on , invariant under the linear action of the group . Combs are characterized by the additional requirement of being measures supported in : their decomposition into homogeneous components involves the family , of Eisenstein distributions, and the coefficients of the decomposition are given as Dirichlet series . Functional equations of the usual (Hecke) kind relative to turn out to be equivalent to the invariance of the comb under some modification...
We establish the spectral gap property for dense subgroups of SU, generated by finitely many elements with algebraic entries; this result was announced...
We present in this paper a stability study concerning finite volume schemes applied to the two-dimensional Maxwell system, using rectangular or triangular meshes. A stability condition is proved for the first-order upwind scheme on a rectangular mesh. Stability comparisons between the Yee scheme and the finite volume formulation are proposed. We also compare the stability domains obtained when considering the Maxwell system and the convection equation.
Suppose is an abelian extension of number fields. Stark’s conjecture predicts, under suitable hypotheses, the existence of a global unit of such that the special values for all characters of can be expressed as simple linear combinations of the logarithms of the different absolute values of .In this paper we formulate an extension of this conjecture, to attempt to understand the values when the order of vanishing may be greater than one. This conjecture no longer predicts the existence...
According to the well-known Nyman-Beurling criterion the Riemann hypothesis is equivalent to the possibility of approximating the characteristic function of the interval in mean square norm by linear combinations of the dilations of the fractional parts for real greater than . It was conjectured and established here that the statement remains true if the dilations are restricted to those where the ’s are positive integers. A constructive sequence of such approximations is given.