Related papers: Inverse Erdos-Fuchs theorem for k-fold sumsets

We use the definition of a fractional integral, recently proposed by Katugampola, to establish a generalization of the reverse Minkowski's inequality. We show two new theorems associated with this inequality, as well as state and show other…

We prove that the structure of right generalized inverse semigroups is determined by free \'etale actions of inverse semigroups. This leads to a tensor product interpretation of Yamada's classical struture theorem for generalized inverse…

We generalize results of Duke, Garcia, Hyde, Lutz and others on the distribution of sums of roots of unity related to Gaussian periods to obtain equidistribution of similar sums over zeros of arbitrary integral polynomials. We also…

In this note, we give a shorter proof of the result of Zheng, Yu, and Pei on the explicit formula of inverses of generalized cyclotomic permutation polynomials over finite fields. Moreover, we characterize all these cyclotomic permutation…

In this paper, we establish some general Kastler-Kalau-Walze type theorems for any dimensional manifolds with boundary which generalize the results in [WW1].

We show the recurrence relations of the Euler-Zagier multiple zeta-function which describes the $r$-fold function with one variable specialized to a non-positive integer as a rational linear combination of $(r-1)$-fold functions, which…

We prove a generalization of Gowers' theorem for $\mathrm{FIN}_{k}$ where, instead of the single tetris operation $T:\mathrm{FIN}_{k}\rightarrow \mathrm{FIN}_{k-1}$, one considers all maps from $\mathrm{FIN}_{k}$ to $\mathrm{FIN}_{j}$ for…

We show that Mandell's inverse $K$-theory functor from $\Gamma$-categories to permutative categories preserves multiplicative structure. This is a first step towards an equivariant generalization that would be inverse to the construction of…

Here we simplify the proof of the de Rham theorem for Schwartz functions on affine Nash manifolds and generalize the result to the case of non affine Nash manifolds.

We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.

We consider the generalized weighted zeta function for a finite digraph, and show that it has the Ihara expression, a determinant expression of graph zeta functions, with a certain specified definition for inverse arcs. A finite digraph in…

We provide a finite-dimensional model of the twisted K-group twisted by any degree three integral cohomology class of a CW complex. One key to the model is Furuta's generalized vector bundle, and the other is a finite-dimensional…

Hadamard's global inverse theorem provides conditions for a function to be globally invertible on Rn. In this note we show that the conditions are robust enough for the conclusion to hold even if we relax the conditions by removing the…

We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…

Let $A$ be a subset of a finite field $F := \Z/q\Z$ for some prime $q$. If $|F|^\delta < |A| < |F|^{1-\delta}$ for some $\delta > 0$, then we prove the estimate $|A+A| + |A.A| \geq c(\delta) |A|^{1+\eps}$ for some $\eps = \eps(\delta) > 0$.…

We develop a simple and intuitive identity for calculating expectations of weighted $k$-fold sums over particles in branching processes, generalising the well-known many-to-one lemma.

We prove a structural theorem for generalized arithmetic progressions in $\F_p$ which contain a large product set of two other progressions.

In 1971, Ruzsa conjectured that if $f:\ \mathbb{N}\rightarrow\mathbb{Z}$ with $f(n+k)\equiv f(n)$ mod $k$ for every $n,k\in\mathbb{N}$ and $f(n)=O(\theta^n)$ with $\theta<e$ then $f$ is a polynomial. In this paper, we investigate the…

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local…

Using methods of KK-theory, we generalize Poincare duality to the framework of twisted K-theory.