Counting Additive Decompositions of Quadratic Residues in Finite Fields

We say that a set $S$ is additively decomposed into two sets $A$ and $B$ if $S = \{a+b : a\in A, \ b \in B\}$. A. S\'ark\"ozy has recently conjectured that the set $Q$ of quadratic residues modulo a prime $p$ does not have nontrivial decompositions. Although various partial results towards this conjecture have been obtained, it is still open. Here we obtain a nontrivial upper bound on the number of such decompositions

Current non-conservation effects in ν\nuDIS diffraction

In the neutrino DIS diffraction the charged current non-conservation gives rise to sizable corrections to the longitudinal structure function, $F_L$. These corrections is a higher twist effect enhanced at small-$x$ by the rapidly growing gluon density. The phenomenon manifests itself in abundant production of charm and strangeness by longitudinally polarized W bosons of moderate virtualities Q^2\lsim m_c^2.Comment: Prepared for the Int. Workshop on Diffraction in High-Energy Physics, Diffraction 2008, La Londe-les-Maures, France, Sept. 9-14, 200

Features of elastic scattering at small t at the LHC

The problems linked with the extraction of the basic parameters of the hadron elastic scattering amplitude at the LHC are explored. It is shown that one should take into account the saturation regime which will lead to new effects at the LHC.Comment: 3. pages, 6 figures, talk on the International workshop on "Diffraction in High Energy Physics", La Londe-les-Maures, France (2008