Math Research: Latest Papers - Nov 27, 2025

Nov 26, 2025 by Alex Johnson 44 views

Welcome to the latest digest of mathematical research! This edition, dated November 27, 2025, showcases a diverse range of topics within number theory, representation theory, and related fields. The following papers offer insights into cutting-edge research. Don't forget to check the Github page for more details and a broader selection of papers.

Dive into the Latest Math.NT and Math.RT Papers

Here’s a glimpse of the most recent publications:

**On the $C^*$ -algebras of linear dynamical systems**

Authors: Ingrid Beltita, Daniel Beltita
Category: math.OA
Date: 2025-11-25
Comment: 9 pages

This paper explores the properties of $C^*$ -algebras generated by linear dynamical systems. The authors confirm a conjecture about continuous-trace subquotients and also determine that the dimension of the ambient vector space can be recovered from the corresponding $C^*$ -algebra. Furthermore, the paper provides a rigidity result for certain nilpotent actions.

Hearing the Serre invariant of a compact $p$ -adic analytic manifold

Authors: Patrick Erik Bradley, Ángel Morán Ledezma
Category: math.NT
Date: 2025-11-25
Comment: 12 pages

This research uses a unique method for defining kernel functions for Laplacian integral operators on compact $p$ -adic analytic manifolds. The authors apply one such operator to investigate the Serre invariant, linking it to the wavelet spectrum and the number of rational points of elliptic curves over $p$ -adic fields. The study reveals a connection between the Serre invariant and the wavelet spectrum of a specific operator, particularly in the context of elliptic curves with split multiplicative reduction.

Algebraic functions and class number formulas

Authors: Sushmanth J. Akkarapakam, Patrick Morton
Category: math.NT
Date: 2025-11-25
Comment: 44 pages, 4 tables

This paper provides a class number formula for extended ring class fields over imaginary quadratic fields. It involves determining fields generated by the periodic points of an algebraic function. The number of periodic points is related to the sum of class numbers of imaginary quadratic orders. The research focuses on class number formulas for extended ring class fields over imaginary quadratic fields. This is achieved by analyzing the periodic points of a carefully selected algebraic function.

Isogeny graphs of superspecial abelian varieties and Brandt matrices

Authors: Bruce W. Jordan, Yevgeny Zaytman
Category: math.NT
Date: 2025-11-25

This work examines isogeny graphs associated with principally polarized abelian varieties. It defines and analyzes three isogeny graphs, proving their connectivity and linking them to Brandt matrices. The adjacency matrices of the three isogeny graphs are expressed using Brandt matrices, defined by Hashimoto, Ibukiyama, Ihara, and Shimizu. Furthermore, the researchers delve into the properties of these Brandt matrices and reframe the theory using the concept of Brandt graphs. The study provides the $\ell$ -adic uniformization of $\mathit{gr}\_g(\ell,p)$ and $\widetilde{\mathit{gr}}\_g(\ell,p)$ .

The Weyl bound for Rankin-Selberg $L$ -functions with Joint Ramification

Authors: Yunjian Peng
Category: math.NT
Date: 2025-11-25
Comment: 30 pages

This paper establishes the Weyl bound for the Rankin-Selberg $L$ -function within a joint ramification setting. It uses the refined Petersson trace formula and a special Voronoï summation formula to achieve this result. The paper establishes the Weyl bound for the Rankin-Selberg $L$ -function. To achieve this result, the authors use the refined Petersson trace formula and develop a special Voronoï summation formula.

Invertible Orbifolds over Finite Fields

Authors: Marco Aldi, Andrija Perunicic
Category: math.NT
Date: 2025-11-25
Comment: 17 pages

This research calculates the eigenvalues of the Frobenius endomorphism acting on a $p$ -adic version of Borisov's complex in the context of Berglund-Huebsch mirror symmetry. As a result, the authors propose an explicit formula for the number of points of crepant resolutions of invertible Calabi-Yau orbifolds defined over a finite field. The work focuses on computing the eigenvalues of the Frobenius endomorphism in the context of Berglund-Huebsch mirror symmetry, and the findings result in a formula for calculating the number of points of crepant resolutions of invertible Calabi-Yau orbifolds over a finite field.

Parametric Algorithms for the 5-Modular Analog of ES (Sierpiński): Structure of Solutions, Parameterization, and Constructive Proofs (SERP)

Authors: E. Dyachenko
Category: math.NT
Date: 2025-11-25

This paper investigates the representation of the fraction 5/P as a sum of three distinct unit fractions. It analyzes cases of primes congruent to 1 mod 5, developing parametric constructions and enumeration algorithms. The study extends previous work for coefficient 4 (the Erdős–Straus conjecture) to coefficient 5, transferring the same structure of parametrization and constructive solutions. Moreover, the analytic applications provide averaging tools used for density estimates in parametric boxes.

Arithmetic Sparsity and Obstructions in Weighted Projective Spaces

Authors: Tanush Shaska
Category: math.NT
Date: 2025-11-25

This paper examines the distribution of rational and algebraic points of bounded weighted height in weighted projective spaces. The study derives an asymptotic formula for counting such points and provides a cohomological interpretation, analogous to the Brauer-Manin obstruction. The work offers a weighted version of the Batyrev-Manin conjecture and explores potential applications in moduli theory and arithmetic geometry. The paper investigates the distribution of rational and algebraic points in weighted projective spaces and derives an asymptotic formula for counting such points.

On lattices over Fermat function fields

Authors: Rafael Froner Prando, Pietro Speziali
Category: math.AG
Date: 2025-11-25
Comment: 20 pages

This paper constructs a new family of lattices arising from the Fermat function field and its inflection points. The lattices have a specific rank, and their minimum distance is determined. The results provide examples of function field lattices of large rank whose minimum distance surpasses the expected bound. The paper constructs a new family of lattices based on the Fermat function field. They determine the minimum distance and kissing number, and analyze the structure of the second shortest vectors.

Fast evaluation of Riemann theta functions in any dimension

Authors: Noam D. Elkies, Jean Kieffer
Category: math.NT
Date: 2025-11-25

This research describes an algorithm to numerically evaluate Riemann theta functions in quasi-linear time. The algorithm is implemented in the FLINT number theory library and is used to evaluate theta constants, constructing polynomials of degree 65. The work describes an algorithm to numerically evaluate Riemann theta functions, and the algorithm is implemented in the FLINT number theory library.

Solubility of a family of conics with polynomial coefficients in many variables

Authors: Mathieu Da Silva
Category: math.NT
Date: 2025-11-25

This paper studies the proportion of conics that have a rational point. It provides an asymptotic formula for the number of points with bounded height. The research investigates the proportion of conics having a rational point and provides an asymptotic formula for the number of points with bounded height.

Arithmetic compactifications of integral models of Shimura varieties of abelian type

Authors: Peihang Wu
Category: math.NT
Date: 2025-11-25
Comment: v2: 151 pages. minor changes on typos. Added: A workflow diagram; Section 5.5 on nearby cycles

This paper constructs toroidal and minimal compactifications for integral models of abelian-type Shimura varieties. The research studies the action of points of the adjoint group on boundary charts and toroidal compactifications. This research constructs compactifications for integral models of Shimura varieties.

Serre's uniformity question and proper subgroups of $C_{ns}^+(p)$

Authors: Lorenzo Furio, Davide Lombardo
Category: math.NT
Date: 2025-11-25
Comment: 35 pages. Final version, to appear in Algebra & Number Theory

This paper addresses Serre's uniformity question, investigating the image of residual Galois representations of elliptic curves. The authors strengthen previous results by showing that the image of the representation is not conjugate to a specific subgroup for primes larger than 5.

The asymptotic distribution of Elkies primes for reductions of abelian varieties is Gaussian

Authors: Alexandre Benoist, Jean Kieffer
Category: math.NT
Date: 2025-11-25

This research generalizes the notion of Elkies primes to abelian varieties with real multiplication. It proves that the number of Elkies primes converges weakly to a Gaussian distribution. This work provides a generalization of Elkies primes to abelian varieties and proves that the number of Elkies primes converges to a Gaussian distribution.

The Balmer spectrum and tensor telescope conjecture for noetherian path algebras

Authors: Enrico Sabatini
Category: math.RT
Date: 2025-11-25
Comment: 18 pages

This paper studies the tensor triangulated category. The research finds a description of the internal hom functor and computes its Balmer spectrum. This paper studies the tensor triangulated category and computes its Balmer spectrum.

Hochschild cohomology of Beilinson algebras of graded down-up algebras with weights ( $n,m$ )

Authors: Ayako Itaba, Shu Minaki
Category: math.RA
Date: 2025-11-25

This research gives the dimensional formula of the Hochschild cohomology group for Beilinson algebras of graded down-up algebras. Furthermore, the study gives the ring structure on the Hochschild cohomology group for a specific case. This paper provides the dimensional formula of the Hochschild cohomology group for Beilinson algebras.

Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules

Authors: Dražen Adamović, Sven Möller
Category: math.QA
Date: 2025-11-25
Comment: 43 pages, LaTeX

This work proposes a connection between affine vertex operator algebras and Virasoro minimal models. It is based on character identities and relates affine vertex operator algebras to rational minimal models. The character identities extend to certain abelian intertwining algebras. This paper proposes a connection between affine vertex operator algebras and Virasoro minimal models.

Designs on the Tautological bundle

Authors: Ikeda Yuya
Category: math.CO
Date: 2025-11-25

This paper introduces the framework of a generalized design and constructs such a design on the space of sections of the tautological bundle over the complex projective line. The construction relies on invariant theory for the binary icosahedral group. This paper introduces the framework of a generalized design and constructs such a design on the space of sections of the tautological bundle.

Zeta Zeros on the Critical Line

Authors: Daniel A. Goldston, Ade Irma Suriajaya
Category: math.NT
Date: 2025-11-25
Comment: expository note, content is 6 pages (total 7 pages)

This expository note discusses the distribution of Riemann zeta-function zeros. It explains that if the Riemann Hypothesis could be removed from Montgomery's simple zero proof, this would also give a proof that 2/3 of the zeros are on the critical line. This paper discusses the distribution of Riemann zeta-function zeros.

Real convergence and periodicity of $p$ -adic continued fractions

Authors: Giuliano Romeo
Category: math.NT
Date: 2025-11-25

This paper explores the connection between periodic $p$ -adic continued fractions and convergence to real quadratic irrationals. The research shows a strong connection between periodic $p$ -adic continued fractions and the convergence to real quadratic irrationals.

This collection offers a glimpse into the diverse and active areas of mathematical research. For a more detailed view and access to the complete papers, please visit the links provided and the Github page.

For further reading, consider exploring the ArXiv website, which is a key resource for preprints in mathematics and physics.