471,771 research outputs found
Average prime-pair counting formula
Taking , let denote the number of prime pairs
with . The prime-pair conjecture of Hardy and Littlewood (1923) asserts
that with an explicit constant
. There seems to be no good conjecture for the remainders
that corresponds to
Riemann's formula for . However, there is a heuristic
approximate formula for averages of the remainders which is
supported by numerical results.Comment: 26 pages, 6 figure
Simple linear compactifications of odd orthogonal groups
We classify the simple linear compactifications of SO(2r+1), namely those
compactifications with a unique closed orbit which are obtained by taking the
closure of the SO(2r+1)xSO(2r+1)-orbit of the identity in a projective space
P(End(V)), where V is a finite dimensional rational SO(2r+1)-module.Comment: v2: several simplifications, final version. To appear in J. Algebr
Differential operator realizations of superalgebras and free field representations of corresponding current algebras
Based on the particular orderings introduced for the positive roots of finite
dimensional basic Lie superalgebras, we construct the explicit differential
operator representations of the and superalgebras
and the explicit free field realizations of the corresponding current
superalgebras and at an arbitrary level .
The free field representations of the corresponding energy-momentum tensors and
screening currents of the first kind are also presented.Comment: Latex file; 41 pages; V2, typos correcte
Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N=2 Gauge Theories with Classical Gauge Groups
N=2 Seiberg-Witten theories allow an interesting interplay between the
Argyres-Douglas loci, singularity structures and wall-crossing formulae. In
this paper we investigate this connection by first studying the singularity
structures of hyper-elliptic Seiberg-Witten curves for pure N=2 gauge theories
with SU(r+1) and Sp(2r) gauge groups, and propose new methods to locate the
Argyres-Douglas loci in the moduli space, where multiple mutually non-local BPS
states become massless. In a region of the moduli space, we compute dyon
charges for all 2r+2 and 2r+1 massless dyons for SU(r+1) and Sp(2r) gauge
groups respectively for rank r>1. From here we elucidate the connection to the
wall-crossing phenomena for pure Sp(4) Seiberg-Witten theory near the
Argyres-Douglas loci, despite our emphasis being only at the massless sector of
the BPS spectra. We also present 2r-1 candidates for the maximal
Argyres-Douglas points for pure SO(2r+1) Seiberg-Witten theory.Comment: 81 pages, 41 figures, LaTeX; v2: Minor cosmetic changes and
correction of a typographical error in acknowledgement. Final version to
appear in JHE
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