Results 81 to 90 of about 31,249 (173)
Polymatroidal tilings and the Chow class of linked projective spaces
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract Linked projective spaces are quiver Grassmannians of constant dimension one of certain quiver representations, called linked nets, over certain quivers, called Zn$\mathbb {Z}^n$‐quivers. They were recently introduced as a tool for describing schematic limits of families of divisors.
Felipe de Leon, Eduardo Esteves
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The fundamental group of the complement of a generic fiber‐type curve
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract In this paper, we describe and characterize the fundamental group of the complement of generic fiber‐type curves, that is, unions of (the closure of) finitely many generic fibers of a component‐free pencil F=[f:g]:CP2⤍CP1$F=[f:g]:\mathbb {C}\mathbb {P}^2\dashrightarrow \mathbb {C}\mathbb {P}^1$.
José I. Cogolludo‐Agustín +1 more
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On equal consecutive values of multiplicative functions
Discrete AnalysisOn equal consecutive values of multiplicative functions, Discrete Analysis 2024:12, 20 pp. It is widely expected that the prime factorizations of a pair of large consecutive natural numbers $n, n+1$ (or of a pair with fixed spacing, such as $n,n+2 ...
Alexander P. Mangerel
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Continued fractions and q-series generating functions for the generalized sum-of-divisors functions
Journal of Number Theory, 2017 Keywords: divisor function; sum of divisors function; continued fraction; J-fraction.
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Which singular tangent bundles are isomorphic?
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract Logarithmic and b$ b$‐tangent bundles provide a versatile framework for addressing singularities in geometry. Introduced by Deligne and Melrose, these modified bundles resolve singularities by reframing singular vector fields as well‐behaved sections of these singular bundles.
Eva Miranda, Pablo Nicolás
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Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We survey ideas surrounding the study of the number of integers that can be represented as the sum of three positive cubes. We focus on the early contribution of Davenport using elementary techniques, and the subsequent developments due to Vaughan, which introduced Fourier analysis and mirrored many of the important developments of the Hardy ...
James Maynard
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A combinatorial identity for the sum of divisors function involving $p_{r}(n)$
, 2020 Let $\sum_{d|n}d$ denote the sum of divisors of a positive integer $n$, and let $\prod_{j=1}^{\infty}(1-q^{j})^{r}=\sum_{n=0}^{\infty}p_{r}(n)q^{n}$. The aim is of this note is to prove the following interesting combinatorial identity$$\sum_{d|n}d=n\,\sum_{r=1}^{n}\frac{(-1)^{r}}{r}\,\binom{n}{r}\, p_{r}(n).$$
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Some Equations Concerning the Sum of Divisors Function
The PUMP Journal of Undergraduate ResearchIn this article, I wiil consider four equations involving the sum of divisors function, σ, and I will prove that for the first two there are infinitely many solutions, while for the other two I will provide some particular solutions. I will also study some properties regarding two sequences of numbers.
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Sums of divisor functions in $F_{q}[t]$ and matrix integrals
, 2015 We study the mean square of sums of the $k$th divisor function $d_k(n)$ over short intervals and arithmetic progressions for the rational function field over a finite field of $q$ elements. In the limit as $q\rightarrow\infty$ we establish a relationship with a matrix integral over the unitary group.
Keating, Jon +3 more
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Summing μ ( n ) : a faster elementary algorithm. [PDF]
Res Number Theory, 2023 Helfgott HA, Thompson L.
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