Zobrazeno 1 - 10
of 143
pro vyhledávání: '"11D79"'
Autor:
Vlăduţ, Sergei
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
Comment: Many
Comment: Many
Externí odkaz:
http://arxiv.org/abs/2409.12316
Autor:
Baier, Stephan, Chattopadhyay, Aishik
We study small non-trivial solutions of quadratic congruences of the form $x_1^2+\alpha_2x_2^2+\alpha_3x_3^2\equiv 0 \bmod{q}$, with $q$ being an odd natural number, in an average sense. This extends previous work of the authors in which they conside
Externí odkaz:
http://arxiv.org/abs/2408.15360
Autor:
Daras, Nicholas J.
We will construct post-quantum encryption algorithms based on three-variable polynomial Beal-Schur congruence. After giving a proof of Beal's conjecture and citing some applications of it to selected cases where the discrete logarithm and some of its
Externí odkaz:
http://arxiv.org/abs/2409.03758
We prove asymptotic formulae for small weighted solutions of quadratic congruences of the form $\lambda_1x_1^2+\cdots +\lambda_nx_n^2\equiv \lambda_{n+1}\bmod{p^m}$, where $p$ is a fixed odd prime, $\lambda_1,...,\lambda_{n+1}$ are integer coefficien
Externí odkaz:
http://arxiv.org/abs/2406.12758
Autor:
Yip, Chi Hoi, Yoo, Semin
Publikováno v:
Int. J. Number Theory, 2024+
Let $k \geq 2$, $q$ be an odd prime power, and $F \in \mathbb{F}_q[x_1, \ldots, x_k]$ be a polynomial. An $F$-Diophantine set over a finite field $\mathbb{F}_q$ is a set $A \subset \mathbb{F}_q^*$ such that $F(a_1, a_2, \ldots, a_k)$ is a square in $
Externí odkaz:
http://arxiv.org/abs/2406.00310
The well-known result states that the square-free counting function up to $N$ is $N/\zeta(2)+O(N^{1/2})$. This corresponds to the identity polynomial $\text{Id}(x)$. It is expected that the error term in question is $O_\varepsilon(N^{\frac{1}{4}+\var
Externí odkaz:
http://arxiv.org/abs/2405.06969
Autor:
Harm, Michael
Let $G_1,\dots, G_n\in \mathbb{F}_p[X_1,\dots,X_m]$ be $n$ polynomials in $m$ variables over the finite field $\mathbb{F}_p$ of $p$ elements. For any sufficiently large prime $p$ and non-trivial bounds for the Weyl sums associated to the non-trivial
Externí odkaz:
http://arxiv.org/abs/2403.05078
We address three questions posed by Bibak \cite{KB20}, and generalize some results of Bibak, Lehmer and K G Ramanathan on solutions of linear congruences $\sum_{i=1}^k a_i x_i \equiv b \Mod{n}$. In particular, we obtain explicit expressions for the n
Externí odkaz:
http://arxiv.org/abs/2403.01923
In this article, we consider systems of linear congruences in several variables and obtain necessary and sufficient conditions as well as explicit expressions for the number of solutions subject to certain restriction conditions. These results are in
Externí odkaz:
http://arxiv.org/abs/2403.01914
Autor:
Ripà, Marco
For every non-negative integer $a$ and positive integer $b$, the congruence speed of the tetration $^{b}a$ is the difference between the number of the rightmost digits of $^{b}a$ that are the same as those of $^{b+1}a$ and the number of the rightmost
Externí odkaz:
http://arxiv.org/abs/2402.07929