Related papers: Multiplicity One Theorems, S-Version

We will prove several congruences modulo a power of a prime such as $$ \sum_{0<k_1<...<k_{n}<p}\leg{p-k_{n}}{3} {(-1)^{k_{n}}\over k_1... k_{n}}\equiv {lll} -{2^{n+1}+2\over 6^{n+1}} p B_{p-n-1}({1\over 3}) &\pmod{p^2} &{if $n$ is odd}…

We show a new large sieve version of the Brun-Titchmarsh theorem.

In this paper, we can show that \begin{align*} S_{\Lambda}(x)=\sum_{1\leq n\leq x}\Lambda \left(\left[\frac{x}{n}\right]\right)= \sum_{n=1}^{\infty} \frac{\Lambda(n)}{n(n+1)}x +O\left(x^{7/15+1/195+\varepsilon}\right), \end{align*} where…

We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.

In this paper we start with the applications of polyfold theory to symplectic field theory.

This note gives simpler proofs of the variational and multiple priors representations in Maccheroni et al. (2006) and Gilboa and Schmeidler (1989).

We describe polarized complexity-one T-varieties combinatorially in terms of so-called divisorial polytopes, and show how geometric properties of such a variety can be read off the corresponding divisorial polytope. We compare our…

This article introduces three invariance principles under which P is different from NP. In the second part a theorem of convergence is proven. This theorem states that for any language L there exists an infinite sequence of languages from…

It is shown that an application of optical theorem for the non-unitary S-matrix can lead to the qualitative error in the result.

We prove relative versions of many earlier results about almost invariant sets and splittings of groups. In particular, we prove a relative version of the algebraic torus theorem, and we prove the existence and uniqueness of relative…

It is proved that all Jordan s-identities of the three variables are consequences of s-identities Glennie.

We show that the theorem of the three perpendiculars holds in any n-dimensional space form.

In this note we present a proof of multiple recurrence for ergodic systems (and thereby of Szemer\'edi's theorem) being a mixture of three known proofs. It is based on a conditional version of the Jacobs-de Leeuw-Glicksberg decomposition…

We obtain new multilinear multiplier theorems for symbols of restricted smoothness which lie locally in certain Sobolev spaces. We provide applications concerning the boundedness of the commutators of Calder\'on and…

We prove the following generalization of Severi's Theorem: Let $X$ be a fixed complex variety. Then there exist, up to birational equivalence, only finitely many complex varieties $Y$ of general type of dimension at most three which admit a…

Let C be some class of objects equipped with a set of simplifying moves. When we apply these to a given object M in C as long as possible, we get a root of M. Our main result is that under certain conditions the root of any object exists…

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

We prove that the reciprocal sum $S_k(x)$ of the least common multiple of $k\geq 3$ positive integers in $\N\cap [1,x]$ satisfies $$ S_k(x)=P_{2^k-1}(\log x)+O(x^{-\theta_k+\epsilon}) $$ where $P$ is a polynomial of degree $2^k-1$ and…

We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^c case. In particular, we prove a K-theory version of the main results of [{\bf H}], [{\bf Liu1}, Theorem B] for a family of almost complex manifolds.

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.