Zobrazeno 1 - 10
of 548
pro vyhledávání: '"11P55"'
Autor:
Flores, Daniel
We demonstrate the existence of $K$-multimagic squares of order $N$ consisting of distinct integers whenever $N>2 K(K+1)$. This improves upon our earlier result in which we only required $N+1$ distinct integers. Additionally, we present a direct meth
Externí odkaz:
http://arxiv.org/abs/2411.01091
If $\mathscr A$ is a set of natural numbers of exponential density $\delta$, then the exponential density of all numbers of the form $x^3+a$ with $x\in\mathbb N$ and $a\in\mathscr A$ is at least $\min(1, \frac 13+\frac 56 \delta)$. This is a consider
Externí odkaz:
http://arxiv.org/abs/2409.16795
Autor:
Mishra, Hrishabh
We establish new upper bounds on the number of failures of the integral Hasse principle within the family of Markoff type cubic surfaces $x^2+ y^2+ z^2- xyz= a$ with $|a|\leq A$ as $A\to \infty$. Our bound improves upon existing work of Ghosh and Sar
Externí odkaz:
http://arxiv.org/abs/2408.06846
We use the circle method to prove that a density 1 of elements in $\mathbb{F}_q[t]$ are representable as a sum of three cubes of essentially minimal degree from $\mathbb{F}_q[t]$, assuming the Ratios Conjecture and that the characteristic is bigger t
Externí odkaz:
http://arxiv.org/abs/2408.03668
Autor:
Nguyen, Thi Thu
We obtain asymptotic results on the average numbers of Goldbach representations of an interger as the sum of two primes in different arithmetic progressions. We also prove an omega-result showing that the asymptotic result is essentially the best pos
Externí odkaz:
http://arxiv.org/abs/2407.18266
We count integral quaternion zeros of $\gamma_1^2 \pm \dots \pm \gamma_n^2$, giving an asymptotic when $n\ge 9$, and a likely near-optimal bound when $n=8$. To do so, we introduce a new, nonabelian delta symbol method, which is of independent interes
Externí odkaz:
http://arxiv.org/abs/2407.11804
Autor:
Rome, Nick, Yamagishi, Shuntaro
For any $d \geq 2$, we prove that there exists an integer $n_0(d)$ such that there exists an $n \times n$ magic square of $d^\text{th}$ powers for all $n \geq n_0(d)$. In particular, we establish the existence of an $n \times n$ magic square of squar
Externí odkaz:
http://arxiv.org/abs/2406.09364
Autor:
Rome, Nick, Yamagishi, Shuntaro
In this paper, we obtain an asymptotic formula for the number of integral solutions to a system of diagonal equations. We obtain an asymptotic formula for the number of solutions with variables restricted to smooth numbers as well. We improve the req
Externí odkaz:
http://arxiv.org/abs/2406.09256
Autor:
Flores, Daniel
In this paper we investigate $K$-multimagic squares of order $N$, these are $N \times N$ magic squares which remain magic after raising each element to the $k$th power for all $2 \le k \le K$. Given $K \ge 2$, we consider the problem of establishing
Externí odkaz:
http://arxiv.org/abs/2406.08161
Autor:
Bruedern, Joerg, Wooley, Trevor D.
We present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy-Littlewood method. In particular, we derive mean value estimates on major arcs for smooth Weyl sums of degree $k$ delivering essentially optimal bound
Externí odkaz:
http://arxiv.org/abs/2405.18608