Abstract Let p be a fixed odd prime. E an elliptic curve defined over number field F with either good ordinary reduction or multiplicative at each prime of above . We shall study the characteristic element Selmer group -adic Lie extension. In particular, we relate order vanishing these elements evaluated Artin representations to coranks and their twists in intermediate subextensions

We study the problem of encoding the positions the top-k elements of an array A[1..n] for a given parameter 1 ≤ k ≤ n. Specifically, for any i and j, we wish create a data structure that reports the positions of the largest k elements in A[i..j] in decreasing order, without accessing A at query time. This is a natural extension of the well-known encoding range-maxima query problem, where only t...

We call a subset A of the (additive) abelian group G t-independent if for all non-negative integers h and k with h + k ≤ t, the sum of h (not necessarily distinct) elements of A does not equal the sum of k (not necessarily distinct) elements of A unless h = k and the two sums contain the same terms in some order. A weakly t-independent set satisfies this property for sums of distinct terms. We ...