A special case of Vinogradov's mean value theorem
A special class of triangular arrays.
A special prime divisor of the sequence: .
A spectral analysis of automorphic distributions and Poisson summation formulas
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...
A spectral gap theorem in SU
We establish the spectral gap property for dense subgroups of SU, generated by finitely many elements with algebraic entries; this result was announced...
A spectral proof of Rademacher's conjecture for congruence subgroups of the modular group.
A splitting theorem for quadratic forms.
A stability analysis for finite volume schemes applied to the Maxwell system
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.
A Stability Property of the Densest Circle Packing.
A stably free and non-free ring of integers. (Un anneau d'entiers stablement libre et non libre.)
A Stark conjecture “over ” for abelian -functions with multiple zeros
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...
A stationary phase formula for exponential sums over and applications to GL(3)-Kloosterman sums
A statistical density theorem for L-functions with applications
A Stickelberger theorem for p-adic Gauss sums
A stopping time problem on the positive integers
A strategy for proving Riemann hypothesis.
A strengthening of the Nyman-Beurling criterion for the Riemann hypothesis
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.
A structure theorem for sets of lengths
A structure theorem for sets of small popular doubling
We prove that every set A ⊂ ℤ satisfying for t and δ in suitable ranges must be very close to an arithmetic progression. We use this result to improve the estimates of Green and Morris for the probability that a random subset A ⊂ ℕ satisfies |ℕ∖(A+A)| ≥ k; specifically, we show that .
A structure theory for small sum subsets