Generating series for torsion-free bundles over singular curves: rationality, duality and modularity
Y Huang, R Jiang - arXiv preprint arXiv:2312.12528, 2023 - arxiv.org
We consider two motivic generating functions defined on a variety, and reveal their tight
connection. They essentially count torsion-free bundles and zero-dimensional sheaves. On …
connection. They essentially count torsion-free bundles and zero-dimensional sheaves. On …
Statistics of the first Galois cohomology group: a refinement of Malle's conjecture
B Alberts - Algebra & Number Theory, 2022 - msp.org
Malle proposed a conjecture for counting the number of G-extensions L∕ K with
discriminant bounded above by X, denoted N (K, G; X), where G is a fixed transitive …
discriminant bounded above by X, denoted N (K, G; X), where G is a fixed transitive …
Explicit analytic continuation of Euler products
B Alberts - arXiv preprint arXiv:2406.18190, 2024 - arxiv.org
The generating series of a number of different objects studied in arithmetic statistics can be
built out of Euler products. Euler products often have very nice analytic properties, and by …
built out of Euler products. Euler products often have very nice analytic properties, and by …
The proportion of monogenic orders of prime power indices of the pure cubic field
M Kang, D Kim - arXiv preprint arXiv:2306.13295, 2023 - arxiv.org
In this paper, we investigate the proportion of monogenic orders among the orders whose
indices are a power of a fixed prime in a pure cubic field. We prove that the proportion is …
indices are a power of a fixed prime in a pure cubic field. We prove that the proportion is …
[PDF][PDF] A characterization of half-factorial orders in algebraic number fields
B Rago - arXiv preprint arXiv:2304.08099, 2023 - arxiv.org
arXiv:2304.08099v1 [math.AC] 17 Apr 2023 Page 1 arXiv:2304.08099v1 [math.AC] 17 Apr
2023 A CHARACTERIZATION OF HALF-FACTORIAL ORDERS IN ALGEBRAIC NUMBER …
2023 A CHARACTERIZATION OF HALF-FACTORIAL ORDERS IN ALGEBRAIC NUMBER …
[PDF][PDF] Spiral shifting operators from the enumeration of finite-index submodules of Fq [[T]] d
Y Huang, R Jiang - Preprint. https://arxiv. org/abs …, 2023 - yifeng-huang-math.github.io
Fix an integer d≥ 1. We count full-rank Fq [[T]]-submodules of Fq [[T]] d of a given index and
prove a formula analogous to Solomon's formula [26] over Z. We interpret Solomon's method …
prove a formula analogous to Solomon's formula [26] over Z. We interpret Solomon's method …
Most subrings of have large corank
G Chinta, K Isham, N Kaplan - arXiv preprint arXiv:2412.18692, 2024 - arxiv.org
If $\Lambda\subseteq\mathbb {Z}^ n $ is a sublattice of index $ m $, then $\mathbb {Z}^
n/\Lambda $ is a finite abelian group of order $ m $ and rank at most $ n $. Several authors …
n/\Lambda $ is a finite abelian group of order $ m $ and rank at most $ n $. Several authors …
[PDF][PDF] Central values of zeta functions of non-Galois cubic fields
arXiv:2107.10900v2 [math.NT] 31 Jan 2022 Page 1 arXiv:2107.10900v2 [math.NT] 31 Jan
2022 Central values of zeta functions of non-Galois cubic fields Arul Shankar∗, Anders …
2022 Central values of zeta functions of non-Galois cubic fields Arul Shankar∗, Anders …
Weighted enumeration of number fields using Pseudo and Sudo maximal orders
GD Patil - arXiv preprint arXiv:2411.10917, 2024 - arxiv.org
We establish a fundamental theorem of orders (FTO) which allows us to express all orders
uniquely as an intersection ofirreducible orders' along which the index and the conductor …
uniquely as an intersection ofirreducible orders' along which the index and the conductor …
Lower bounds for the number of subrings in Zn
K Isham - Journal of Number Theory, 2022 - Elsevier
Let fn (k) be the number of subrings of index k in Z n. We show that results of Brakenhoff
imply a lower bound for the asymptotic growth of subrings in Z n, improving upon lower …
imply a lower bound for the asymptotic growth of subrings in Z n, improving upon lower …