相关论文: An x-ray estimate in $R^n$

Objectives: A systematic study on the general relativistic Poynting-Robertson effect has been developed so far by introducing different complementary approaches, which can be mainly divided in two kinds: (1) improving the theoretical…

Sums of powers $S_p(n)=\sum_{k=1}^n k^p$ can be described by Faulhaber's formula in terms of the Bernoulli numbers. The first cases of this formula admit visual proofs of various kinds, which lead to factorized Faulhaber polynomials. In…

We prove Shokurov's global index conjecture for foliations in dimension at most three. This answers a question of the first author, Meng, and Xie in dimension three. The main result of this paper is partially obtained by generative AI,…

We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier…

We prove a higher order generalization of Glaeser inequality, according to which one can estimate the first derivative of a function in terms of the function itself, and the Holder constant of its k-th derivative. We apply these…

A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.

The Galilean invariance in three dimensional space-time is considered. It appears that the Galilei group in 2+1 dimensions posses a three-parameter family of projective representations. Their physical interpretation is discussed in some…

We improve the estimates in the restriction problem in dimension $n \ge 4$. To do so, we establish a weak version of a $k$-linear restriction estimate for any $k$. The exponents in this weak $k$-linear estimate are sharp for all $k$ and…

We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n^Omega(w). This shows that the simple counting argument that any formula refutable in width w must…

We prove a sharp square function estimate for the cone in $\mathbb{R}^3$ and consequently the local smoothing conjecture for the wave equation in $2+1$ dimensions.

General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…

We prove a numerical characterization of $\mathbb{P}^n$ for varieties with at worst isolated local complete intersection quotient singularities. In dimension three, we prove such a numerical characterization of $\mathbb{P}^3$ for normal…

A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with the help of a family of weight functions is considered in this paper. For…

We study the gravitational waves in spacetimes of arbitrary dimension. They generalize the pp-waves and the Kundt waves, obtained earlier in four dimensions. Explicit solutions of the Einstein and Einstein-Maxwell equations are derived for…

We extend the isotonic analysis for Wicksell's problem to estimate a regression function, which is motivated by the problem of estimating dark matter distribution in astronomy. The main result is a version of the Kiefer--Wolfowitz theorem…

In this note, we consider the truncated Karhunen-Lo\`eve expansion for approximating solutions to infinite dimensional inverse problems. We show that, under certain conditions, the bound of the error between a solution and its…

A representation of the sharp coefficient in a pointwise estimate for the gradient of the generalized Poisson integral of a function $f$ on ${\mathbb R}^n$ is obtained under the assumption that $f$ belongs to $L^p$. The explicit value of…

In this note, making use of noncommutative $l$-adic cohomology, we extend the generalized Riemann hypothesis from the realm of algebraic geometry to the broad setting of geometric noncommutative schemes in the sense of Orlov. As a first…

We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the…

We generalize a size-biased distribution related to the Riemann xi function using the work of Ferrar. Some analysis and properties of this more general distribution are offered as well.