42,299 research outputs found
A proof of the conjecture of Cohen and Mullen on sums of primitive roots
We prove that for all , every non-zero element in the finite field
can be written as a linear combination of two primitive roots
of . This resolves a conjecture posed by Cohen and Mullen.Comment: 8 pages; to appear in Mathematics of Computatio
On Grosswald's conjecture on primitive roots
Grosswald's conjecture is that , the least primitive root modulo ,
satisfies for all . We make progress towards
this conjecture by proving that for all and for all .Comment: 7 page
On consecutive primitive elements in a finite field
For an odd prime power with we prove that there are always three
consecutive primitive elements in the finite field . Indeed,
there are precisely eleven values of for which this is false. For
we present conjectures on the size of such that
guarantees the existence of consecutive primitive elements in
, provided that has characteristic at
least~. Finally, we improve the upper bound on for all .Comment: 10 pages, 2 table
Treatment of the infrared contribution: NLO QED evolution as a pedagogic example
We show that the conventional prescription used for DGLAP parton evolution at
NLO has an inconsistent treatment of the contribution from the infrared (IR)
region. We illustrate the problem by studying the simple example of QED
evolution, treating the electron and photon as partons. The deficiency is not
present in a physical approach which removes the IR divergency and allows
calculation in the normal 4-dimensional space.Comment: 15 pages, 2 figures, erratum at the end of the articl
Improving the Drell-Yan probe of small x partons at the LHC via a k_t cut
We show that the observation of the Drell-Yan production of low-mass
lepton-pairs (M 3) at the LHC can make a
direct measurement of parton distribution functions (PDFs) in the low x region,
x < 10^{-4}. We describe a procedure that greatly reduces the sensitivity of
the predictions to the choice of the factorization scale and, in particular,
show how, by imposing a cutoff on the transverse momentum of the lepton-pair,
the data are able to probe PDFs in the important low scale, low x domain. We
include the effects of the Sudakov suppression factor.Comment: 14 pages, 5 figures, version to be published in EPJC, with expanded
explanatio
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