Related papers: Some cases of Vojta's Conjecture on integral point…

In two previous papers we showed that any analytically integrable vector field admits a local analytic Poincar\'e-Birkhoff normalization in the neighborhood of a singular point. The aim of this paper is to extend this analytic normalization…

We prove the famous Faber intersection number conjecture and other more general results by using a recursion formula of $n$-point functions for intersection numbers on moduli spaces of curves. We also present some vanishing properties of…

We correct an inaccuracy in the original proof

In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.

We develop the theory of root clusters further in this article and give some applications. We introduce some new notions as well as recall earlier notions for field extensions over a perfect base field: root cluster size, its generalization…

We estimate the proportion of function fields satisfying certain conditions which imply a function-field analogue of the Fontaine-Mazur conjecture. As a byproduct, we compute the fraction of abelian varieties (or even Jacobians) over a…

Fujita's conjecture is known to be false in positive characteristic. We conjecture and give an approach to a new variant of Fujita's conjecture for the basepoint-freeness, very ampleness, and jet ampleness of linear systems of the form…

Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…

We prove the Tate conjecture for integral degree 4 classes on a smooth cubic hypersurface X of dimension 4 over an algebraic closure of a field finitely generated over its prime subfield.

The heights of iterates of the discrete Painleve equations over number fields appear to grow no faster than polynomials while the heights of generic solutions of non-integrable discrete equations grow exponentially. This gives rise to a…

Some improvements of Young inequality and its reverse for positive numbers with Kontrovich constant are given. Using these inequalities some operator versions and Hilbert-Schmidt norm versions for matrices are proved.

Using the Racah coefficients in our earlier paper arXiv:1107.3918, we explicitly write the Chern-Simons field theory invariants for many non-torus knot and links. Further, we have tabulated the reformulated invariants which agrees with the…

This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…

Withdrawn by the author in favour of math.GT/0511602

We introduce the notion of maximal orders over quaternion algebras with orthogonal involution and give a classification over local fields, and a partial classification over algebraic number fields.

Let $A$ be an abelian variety over the function field $K$ of a compact Riemann surface $B$. Fix a model $f \colon \mathcal{A} \to B$ of $A/K$ and an effective horizontal divisor $\mathcal{D} \subset \mathcal{A}$. We study $(S,…

By restricting the variables running over various (possibly different) subfields, we introduce the notion of a partial zeta function. We prove that the partial zeta function is rational in an interesting case, generalizing Dwork's well…

We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) the analogue of the Riemann…

The property 4 in Proposition 2.3 from the paper "Some remarks on Davie's uniqueness theorem" is replaced with a weaker assertion which is sufficient for the proof of the main results. Technical details and improvements are given.

Towards the Lang--Vojta conjecture, we prove results on finiteness and Zariski degeneracy of $S$-integral points of varieties over number fields $k$, including many cases with geometrically irreducible boundary divisors. Our approach builds…