13,445 research outputs found
Dense sets of integers with prescribed representation functions
Let A be a set of integers and let h \geq 2. For every integer n, let r_{A,
h}(n) denote the number of representations of n in the form n=a_1+...+a_h,
where a_1,...,a_h belong to the set A, and a_1\leq ... \leq a_h. The function
r_{A,h} from the integers Z to the nonnegative integers N_0 U {\infty} is
called the representation function of order h for the set A. We prove that
every function f from Z to N_0 U {\infty} satisfying liminf_{|n|->\infty} f
(n)\geq g is the representation function of order h for some sequence A of
integers, and that A can be constructed so that it increases "almost" as slowly
as any given B_h[g] sequence. In particular, for every epsilon >0 and g \geq
g(h,epsilon), we can construct a sequence A satisfying r_{A,h}=f and A(x)\gg
x^{(1/h)-epsilon}.Comment: 10 page
Some results on rational surfaces and Fano varieties
The goal of this article is to study the equations and syzygies of embeddings
of rational surfaces and certain Fano varieties. Given a rational surface X and
an ample and base-point-free line bundle L on X, we give an optimal numerical
criterion for L to satisfy property Np. This criterion turns out to be a
characterization of property Np if X is anticanonical. We also prove syzygy
results for adjunction bundles and a Reider type theorem for higher syzygies.
For certain Fano varieties we also prove results on very ampleness and higher
syzygies.Comment: 26 pages, AMSTe
On the monotonicity of the correction term in Ramanujan's factorial approximation
We present two new proofs of the monotonicity of the correction term
in Ramanujan's refinement of Stirling's formula.Comment: Latex, 5 page
Compatibility of CAST search with axion-like interpretation of PVLAS results
The PVLAS collaboration has results that may be interpreted in terms of a
light axion-like particle, while the CAST collaboration has not found any
signal of such particles. We propose a particle physics model with paraphotons
and with a low energy scale in which this apparent inconsistency is
circumvented.Comment: 10 pages, 3 figures, version accepted for publication in Physical
Review Letter
- …