ar X iv : m at h / 06 09 13 5 v 1 [ m at h . C O ] 5 S ep 2 00 6 Score sets in oriented bipartite graphs

ar X iv : m at h / 06 09 42 6 v 3 [ m at h . C O ] 1 5 O ct 2 00 6 SUM - PRODUCT ESTIMATES IN FINITE FIELDS VIA KLOOSTERMAN

We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.

ar X iv : m at h / 06 09 42 6 v 2 [ m at h . C O ] 5 O ct 2 00 6 SUM - PRODUCT ESTIMATES IN FINITE FIELDS VIA KLOOSTERMAN

We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.

ar X iv : h ep - p h / 06 09 07 7 v 1 7 S ep 2 00 6 Hadron multiplicities in e + e − annihilation with heavy primary quarks

ar X iv : m at h / 04 09 02 9 v 1 [ m at h . A G ] 2 S ep 2 00 4 ACM BUNDLES ON GENERAL HYPERSURFACES IN P 5 OF LOW DEGREE

In this paper we show that on a general hypersurface of degree r = 3, 4, 5, 6 in P 5 a rank 2 vector bundle E splits if and only if h 1 E(n) = h 2 E(n) = 0 for all n ∈ Z. Similar results for r = 1, 2 were obtained in [15], [16] and [1].

ar X iv : h ep - t h / 06 03 12 5 v 1 1 5 M ar 2 00 6 hep - th / 0603125 ITP – UH – 05 / 06 Noncommutative Instantons on C

We construct explicit solutions of the Hermitian Yang-Mills equations on the noncommutative space C θ . In the commutative limit they coincide with the standard instantons on CP written in local coordinates.