Zobrazeno 1 - 10
of 538
pro vyhledávání: '"11P21"'
Integer geometry on a plane deals with objects whose vertices are points in $\mathbb Z^2$. The congruence relation is provided by all affine transformations preserving the lattice $\mathbb Z^2$. In this paper we study circumscribed circles in integer
Externí odkaz:
http://arxiv.org/abs/2412.04662
Autor:
Kitajima, Masaya
Let be $p$ and $r$ positive real numbers. Then, we consider the lattice point problem of the closed curve $p$-circle $\{x\in\mathbb{R}^{2}|\ |x_{1}|^{p}+|x_{2}|^{p}=r^{p}\}$ which is a generalization of the circle ($p=2$). Following the harmonic anal
Externí odkaz:
http://arxiv.org/abs/2411.10850
Autor:
Temur, Faruk, Sahillioğulları, Cihan
In this article we study two fundamental problems on exponential sums via randomization of frequencies with stochastic processes. These are the Hardy-Littlewood majorant problem, and $L^{2n}(\mathbb{T}), \ n\in \mathbb{N}$ norms of exponential sums,
Externí odkaz:
http://arxiv.org/abs/2411.06517
Autor:
Das, Jishu
Let $F$ be a multi-quadratic totally real number field. Let $\sigma_1,\dots, \sigma_r$ denote its distinct embeddings. Given $s \in F,$ we give an explicit formula for $\| \sigma(s)\|$ and $\sum_{i
Externí odkaz:
http://arxiv.org/abs/2411.02575
Autor:
Cobeli, Cristian, Zaharescu, Alexandru
For any odd prime $p$ and any integer $N\ge 0$, let $\mathcal{V}(p,N)$ be the set of vertices of the cyclotomic box $\mathscr{B} = \mathscr{B}(p,N)$ of edge size $2N$ and centered at the origin $O$ of the ring of integers $\mathbb{Z}[\omega]$ of the
Externí odkaz:
http://arxiv.org/abs/2410.14473
Autor:
Guria, Rachita
We obtain an asymptotic formula with a power-saving error term for counting the integer points $(a,b,c,d)$ in an expanding box $[-X,X]^4$ that satisfy the determinant equation $x_1x_2-x_3x_4=r$ for $r \neq 0$ with two of entries to be prime. The meth
Externí odkaz:
http://arxiv.org/abs/2410.10856
Autor:
Ganguly, Satadal, Guria, Rachita
We obtain an asymptotic formula with an error term for counting integer points $(a, b, c, d)$ in an expanding box $ [-X, X]^4$ that lie on the determinant surface $xy-zw=r$ for $r\neq 0$. The method involves Poisson summation formula, stationary phas
Externí odkaz:
http://arxiv.org/abs/2410.04637
Autor:
Nathanson, Melvyn B.
Shnirel'man's inequality and Shnirel'man's basis theorem are fundamental results about sums of sets of positive integers in additive number theory. It is proved that these results are inherently order-theoretic and extend to partially ordered abelian
Externí odkaz:
http://arxiv.org/abs/2409.16233
Autor:
Kitajima, Masaya
The lattice point problems of the p-circle (e.g., the astroid), which a generalized circle for positive real numbers p, have been solved for approximately p more than 3, based on the series representation of the error term using the generalized Besse
Externí odkaz:
http://arxiv.org/abs/2408.02613
Autor:
Lee, Kyungyong, Li, Li
Let $(F,G)$ be a Jacobian pair with $d=w\text{-deg}(F)$ and $e=w\text{-deg}(G)$ for some direction $w$. A generalized Magnus' formula approximates $G$ as $\sum_{\gamma\ge 0} c_\gamma F^{\frac{e-\gamma}{d}}$ for some complex numbers $c_\gamma$. We dev
Externí odkaz:
http://arxiv.org/abs/2408.01279