ar X iv : m at h / 06 10 37 5 v 1 [ m at h . C V ] 1 1 O ct 2 00 6 Classification of Levi degenerate homogeneous CR - manifolds in dimension 5

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 08 37 7 v 1 [ m at h . R T ] 1 5 A ug 2 00 6 ALGEBRAS OF DERIVED DIMENSION ZERO

ar X iv : m at h / 06 10 28 4 v 1 [ m at h . SG ] 9 O ct 2 00 6 A UNIQUE DECOMPOSITION THEOREM FOR TIGHT CONTACT 3 - MANIFOLDS

It has been shown by V. Colin that every tight contact 3-manifold can be written as a connected sum of prime manifolds. Here we prove that the summands in this decomposition are unique up to order and contactomor-phism.

ar X iv : m at h / 06 05 37 9 v 1 [ m at h . R A ] 1 5 M ay 2 00 6 AN EXTENDED FREUDENTHAL MAGIC SQUARE IN CHARACTERISTIC 3

Date: May 15, 2006. 2000 Mathematics Subject Classification. Primary 17B25.

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.