arXiv math.NT Number Theory
@mathNTb
Followers
2K
Following
0
Media
0
Statuses
53K
Unofficial bot by @vela with https://t.co/qRyAuN2QxC. @mathMPb @mathNAb @mathOAb @mathOCb @mathPRb @mathQAb @mathRAb @mathRTb @mathSGb @mathSPb ...
Joined April 2013
Pacetti, Torcomian: On the generalized Fermat equation of signature $(5,p,3)$ https://t.co/CkZmpT4FCp
https://t.co/fo6wUm8xCi
arxiv.org
In this article we study solutions to the generalized Fermat equation $x^q+y^p+z^r=0 $ using hypergeometric motives within the framework of the modular method. In doing so, we give an explicit...
0
0
10
Kyle Pratt: Cubes from products of terms in progression with one term missing https://t.co/V3IitZk9Tf
https://t.co/fYJn21ElEr
arxiv.org
Let $5 \leq k \leq 11$ and $0\leq i \leq k-1$ be integers. We determine all solutions to the equation \begin{align*} n(n+d)(n+2d)\cdots(n+(i-1)d)(n+(i+1)d) \cdots (n+(k-1)d) = y^3 \end{align*} in...
0
0
6
Bing He, Xiongze Zhang: Proof of a conjecture of Baruah and Sarma on sign patterns of ... https://t.co/OueWnk8mdm
https://t.co/VAvWxnjVBf
arxiv.org
Let \[ \sum_{n=0}^{\infty}A(n)q^{n} := \frac{(q^{2};q^{5})_{\infty}^{5}(q^{3};q^{5})_{\infty}^{5}}{(q;q^{5})_{\infty}^{5}(q^{4};q^{5})_{\infty}^{5}}, \] \[ \sum_{n=0}^{\infty} B(n)q^{n} :=...
0
0
3
Li, Velani, Wang: Intersecting well approximable and missing digit sets https://t.co/Im4naxCCRB
https://t.co/umOMSuQ8s3
arxiv.org
Let $b\geq3$ be an integer and $C(b,D)$ be the set of real numbers in $[0,1]$ whose $b$-ary expansion consists of digits restricted to a given set $D\subseteq\{0,\ldots,b-1\}$. Given an integer...
0
0
2
Preston Tranbarger: Higher Weight Generalized Dedekind Sums https://t.co/sxy2zCdi5G
https://t.co/ENcJHysviA
arxiv.org
Building upon the work of Stucker, Vennos, and Young we derive generalized Dedekind sums arising from period integrals applied to holomorphic Eisenstein series attached to pairs of primitive...
0
0
5
Zhou, Wu: Finite fields whose members are the sum of a potent and a 5-po... https://t.co/MbpJ9FKTxB
https://t.co/66MMHxr55U
arxiv.org
We show that there are only finitely many finite fields whose members are the sum of an $n$-potent element and a $5$-potent element. Combining this with the algorithmic results provided by S.D....
0
1
5
[2025-12-22 Mon (UTC), 6 new articles found for mathNT Number Theory]
0
0
2
Boaz Moerman: $\mathcal{M}$-points of bounded height on toric varieties https://t.co/MkmJlLShGo
https://t.co/epGPQ8qWWu
arxiv.org
We establish an asymptotic formula for the number of $\mathcal{M}$-points of bounded height on split toric varieties, for the height induced by any big and nef divisor class. This formula...
0
1
4
Jie Yang: On the flatness of spin local models for split even orthogonal... https://t.co/4fy6LPACgK
https://t.co/pKKUzdgvfc
arxiv.org
Let $F$ be a complete discretely valued field with ring of integers $\mathcal{O}$ and residue field of characteristic $p>2$. Let $G=\operatorname{GO}_{2n}$ denote the split orthogonal similitude...
0
0
5
Gilles Felber: Symplectic Kloosterman Sums for $\operatorname{Sp}(2n)$ with P... https://t.co/4UX8KOjPdK
https://t.co/JeSOqp6eFr
arxiv.org
We prove a non-trivial bound for $\operatorname{Sp}(2n)$ Kloosterman sums of moduli not equal to a prime multiple of the identity. These sums are attached to Siegel modular forms on the group...
0
0
3
Jie Yang: Topological flatness of orthogonal spin local models https://t.co/09wikXuu3x
https://t.co/OhMHBh8pCs
arxiv.org
Let $p$ be an odd prime and $F$ be a complete discretely valued field with residue field of characteristic $p$. For any parahoric level structure of the split even orthogonal similitude group...
0
0
3
Salami, Zargar: On Properly $\theta$-Congruent Numbers Over Real Number Fields https://t.co/vNHaAmBP93
https://t.co/tDHmCN98Hg
arxiv.org
The notion of $θ$-congruent numbers generalizes the classical congruent number problem. Recall that a positive integer $n$ is $θ$-congruent if it is the area of a rational triangle with...
0
0
3
Salami, Zargar: The splitting fields and Generators of Shioda's elliptic surfa... https://t.co/wsfLl7Zfer
https://t.co/agydgOKPlr
arxiv.org
The splitting field of an elliptic surface $\mathcal E$ defined over ${\mathbb Q}(t)$ is the smallest subfield $\mathcal K$ of $\mathbb C$ such that ${\mathcal E}({\mathbb C}(t))\cong {\mathcal...
0
0
3
Christian T\'afula: A note on the Cram\'er-Granville model https://t.co/4NALus2uuw
https://t.co/nmTwpbaVts
arxiv.org
We show the existence of a set $A\subseteq \mathbb{Z}_{\geq 2}$ satisfying the estimates of the Bateman--Horn conjecture, Goldbach's conjecture, and also \[ \#\{p\leq x \text{ prime} ~|~ p\in...
0
0
2
Li Cai, Taiwang Deng: Distributions of Integral Points and Dedekind Zeta Values https://t.co/EWlp74Tugn
https://t.co/osVw3kZRgb
arxiv.org
We study the distribution of integral matrices with a fixed characteristic polynomial. When the polynomial is irreducible, we determine the leading term of the distribution in terms of zeta...
0
0
4
Florian Pausinger: Counting appearances of integers in sets of arithmetic progres... https://t.co/1zNLkKHys8
https://t.co/ahX57uUu8F
arxiv.org
The sequence $A067549$ of The On-Line Encyclopedia of Integer Sequences is defined as $(a_k)_{k \geq 1}$ with $a_k$ being the determinant of the $k \times k$ matrix whose diagonal contains the...
0
0
6
McGown, Trevi\~no: Polynomial densities and Heilbronn's criterion https://t.co/B04fqUTqvM
https://t.co/mrXOzlKqld
arxiv.org
Heilbronn gave a sufficient condition for a number field with a totally ramified prime to fail to be norm-Euclidean. We say that Heilbronn's criterion applies to a polynomial $f$ if it applies to...
0
0
4
Tristan Phillips: Unbounded average Selmer ranks of elliptic curves in torsion f... https://t.co/48BIJyB5XM
https://t.co/HzFFIGCyfx
arxiv.org
Let $M$ and $N$ be positive integers for which the modular curve $X_1(M,MN)$ has genus $0$, and let $p$ be a prime divisor of $MN$. This article gives asymptotic lower bounds for the average size...
0
1
8
emy Champagne, et al.: Equidistribution of polynomial sequences in function fields: r... https://t.co/fjL2CFJOxo
https://t.co/yKcnwWTKNJ
arxiv.org
Let $\mathbb F_q$ be the finite field of $q$ elements having characteristic $p$, and denote by $\mathbb K_\infty=\mathbb F_q((1/t))$ the field of formal Laurent series in $1/t$. We consider the...
0
0
3