Pure Math · Mathematics & Statistics
Number Theory
The newest papers in Number Theory that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
56 papers, from 1 September 2026 to 3 November 2026: 38 OpenAlex records and 18 arXiv preprints.
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Newest papers
Finding Integer Roots of Polynomials in Nearly Optimal Time
Let $f\in\mathbb Z[x]$ be a polynomial of degree $n$ with integer coefficients of absolute value less than $2^b$.Explicit permutations of $(\mathbb{Z}/4\mathbb{Z})^m$ with uniformly bounded differential uniformity
Symmetric primitives over Galois rings need nonlinear components whose differentials with respect to ring addition are controlled.Good rational functions up to degree six
Locally recoverable codes (LRCs) are fundamental to the architecture of modern distributed storage systems.Cyclotomic polynomials with trinomial irreducible factors over finite fields
We classify the pairs $(q,n)$, where $q$ is a prime power, $n>1$, and $\gcd(n,q)=1$, for which every irreducible factor of $Φ_n(x)$ over $\F_q$ has exactly three nonzero terms.The covering radius of the first-order Reed-Muller code in nine variables is 242
We prove that the covering radius of the binary first-order Reed-Muller code RM(1,9) is exactly 242.Lattice moments and quantum designs
We show that the ensemble of unimodular Gottesman$-$Kitaev$-$Preskill distributions fails to form a rigged quantum $3$-design and quantify the replica defect that determines this failure.Ramanujan Challenge Results: AI-Assisted Evaluation Pipeline for Multi-Format Proofs
As AI's mathematical capabilities rapidly improve, meaningful benchmarks are shifting from university-level problems and math olympiads to research-level mathematics.Goldbach Representations in Quantum Optics and Metrology
We derive a relation between Goldbach representations and photon-number statistics in a quantum-optical setup.Spectral delocalization and central limit theorems for Fourier functionals of stationary Gaussian fields
We characterize Gaussian fluctuations of Fourier-Hermite functionals of stationary Gaussian fields on locally compact Abelian groups via spectral delocalization: conditional on the total spectral…Proofs of strong forms of the Bovdi--Geche universality conjecture and a complex analogue
We prove two universality theorems for neural networks consisting of a single neuron.Contributions to the Stable Derived Categories of Gorenstein Rings
The stable derived category $D_{sg}(R)$ of a Gorenstein ring $R$ is the Verdier quotient of the bounded derived category $D^b(\mathsf{mod}\, R)$ by the thick subcategory of perfect complexes, and…A new lower bound for the sixth Schur number: $S(6)\ge 537$
We give an explicit partition of $\{1,\ldots,537\}$ into six sum-free sets, establishing $S(6)\ge 537$.BCC optimality for the three-dimensional Coulomb lattice energy
We prove that the body-centered cubic lattice uniquely minimizes the renormalized Coulomb energy among three-dimensional Bravais lattices of fixed covolume, up to orthogonal transformations.Near optimal gap in the Lonely Runner Conjecture
For a set $V$ of $n$ distinct positive integers, let $\mathrm{ML}(V)=\max_{t\in\mathbb{R}/\mathbb{Z}}\min_{v\in V}\|vt\|$, where $\|x\|$ is the distance from $x$ to the nearest integer.A simpler proof that there are no Landau--Siegel zeros
This paper simplifies the recent OpenAI proof that there are no Landau--Siegel zeros.Failure of direct finiteness for group algebras in every odd characteristic
For every odd prime $p$, we construct a finitely presented group $G_p$ and elements $a,b,c\in\mathbb{F}_p[G_p]$ such that $ab=1$, $ac=0$, and $c\ne0$.On the Hardy--Littlewood--Chowla conjecture
An old conjecture dating back at least to Hildebrand's work in 1989, asserts that the Möbius function exhibits cancellation on shifted primes; that is, $$\sum_{p\le x}μ(p+2)=o(π(x)),\quad \text{or…On the Lattice Tilings by Lee Balls: Q-Polynomials, Group-Ring Equations, and a Decision Algorithm
More than 50 years ago, Golomb and Welch conjectured that no tilings of $\mathbb{Z}^n$ by Lee balls of radius $r$ exist for $n \geq 3$ and $r \geq 2$.Kaplansky's conjectures fail for torsion-free hyperbolic groups in positive characteristic
Do Kaplansky's group-ring conjectures hold for torsion-free word-hyperbolic groups?Cyclotomic Structure and Exact Recurrences in Floquet Many-Body Quantum Dynamics
Periodically driven quantum systems exhibit a wide range of complex dynamics, including chaos.