ar X iv : m at h - ph / 0 61 00 39 v 1 1 7 O ct 2 00 6 Harmonic analysis on a Galois field and its subfields

ar X iv : h ep - l at / 0 11 00 06 v 1 2 O ct 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : h ep - l at / 0 11 00 06 v 2 3 O ct 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications

ar X iv : m at h - ph / 0 11 00 12 v 1 9 O ct 2 00 1 Functional Equations and Poincare Invariant Mechanical Systems

We study the following functional equation that has arisen in the context of mechanical systems invariant under the Poincaré algebra:

ar X iv : 0 71 1 . 27 39 v 1 [ m at h . N T ] 1 9 N ov 2 00 7 ASYMPTOTIC COHOMOLOGY OF CIRCULAR UNITS

— Let F be a number field, abelian over Q, and fix a prime p 6= 2. Consider the cyclotomic Zp-extension F∞/F and denote Fn the n th finite subfield and Cn its group of circular units. Then the Galois groups Gm,n = Gal(Fm/Fn) act naturally on the Cm’s (for any m ≥ n >> 0). We compute the Tate cohomology groups Ĥ(Gm,n, Cm) for i = −1, 0 without assuming anything else neither on F nor on p.