A class of growth functions u is introduced to construct Hida distributions and test functions. The Legendre transform lu of u is used to define a sequence α(n) = (lu(n)n!), n ≥ 0, of positive numbers. From this sequence we get a CKS-space. Under various conditions on u we show that the associated sequence {α(n)} satisfies those conditions for carrying out the white noise distribution theory on...

Let K be a global field of char p and let Fq be the algebraic closure of Fp in K. For an elliptic curve E/K with non-constant j-invariant, the L-function L(T,E/K) is a polynomial in 1+T ·Z[T ]. For any N > 1 invertible in K and finite subgroup T ⊂ E(K) of order N , we compute the mod N reduction of L(T,E/K) and determine an upper-bound for the order of vanishing at 1/q, the so-called analytic r...