In this paper we extend some results about the probability that the sum of n dependent subexponential random variables exceeds a given threshold u. In particular, the case of non-identically distributed and not necessarily positive random variables is investigated. Furthermore we establish criteria how far the tail of the marginal distribution of an individual summand may deviate from the other...

Concave compositions are compositions (i.e. ordered partitions) of a number in which the parts decrease up to the middle summand(s) and increase thereafter. Perhaps the most surprising result is for even length, concave compositions where the generating function turns out to be the quotient of two instances of the pentagonal number theorem with variations of sign. The false theta function disco...

The function bk(n) is defined as the number of partitions of n that contain no summand divisible by k. In this paper we study the 2-divisibility of b5(n) and the 2and 3-divisibility of b13(n). In particular, we give exact criteria for the parity of b5(2n) and b13(2n).

We prove that if $K$ is a nontrivial null-homotopic knot in closed oriented $3$--manfiold $Y$ such $Y-K$ does not have an $S^1\times S^2$ summand, then the zero surgery on summand. This generalizes result of Hom and Lidman, who proved case when irreducible rational homology sphere.

Let A be a commutative noetherian ring of dimension n. Let P be a projective A[T ]-module. Plumstead ([P]) proved that if rankP > dimA then P splits off a free summand of rank one. It is natural to ask what happens when rankP = dimA. In this paper we investigate this question when P has trivial determinant. Let α : P I be a generic surjection (i.e. I ⊂ A[T ] is an ideal of height n). It is prov...

We show that the Jacobian of a certain Artin-Schreier curve over the field Fp has a a 1-dimensional formal summand of height (p− 1)f for any positive integer f . We give two proofs, the classical one which was known to Manin in 1963 and which requires knowledge of the zeta function of the curve, and a new simpler one using methods of Honda. This is the first step toward contructing the cohomolo...