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.
58 papers, from 1 September 2026 to 3 November 2026: 40 OpenAlex records and 18 arXiv preprints.
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Newest papers, page 2
On the OpenAI proof that Landau-Siegel zeros do not exist
A recent manuscript of OpenAI asserts that Landau-Siegel zeros do not exist.Adjoint Transfer and Order-Lifting Dichotomies for 2 x 2 Matrices over Prime-Power Rings
For an odd prime p, we study the change in matrix order under lifting from Z/p^k Z to Z/p^(k+1) Z. The first variation of the order defect is an affine translate of a cyclic adjoint transfer on…Real Fiducial Vectors Only Exist in Dimensions $d\equiv 3 \pmod{4}$
We investigate restrictions on the dimensions and coordinate fields of real Weyl-Heisenberg fiducial vectors.Improved zero-free half-planes for the quasi-Riemann hypothesis
Recently, a uniform $\frac{7}{8}$ zero-free half-plane for finite-order Hecke $L$-functions over $\mathbb Q(\sqrt{-3})$ and its transfer to Dirichlet $L$-functions was given by OpenAI in [Ope26a].Measurable obstructions for unmeasurable colourings
Due to the availability of powerful analytic techniques, vastly superior lower bounds are known for the measurable chromatic number of Euclidean spaces compared to their ordinary chromatic number.Stability of plethysm coefficients and modified polynomial induction
Let $h_n$ denote the complete homogeneous symmetric function of degree $n$, $s_ν$ the Schur function indexed by a partition $ν$, and $\langle\cdot,\cdot\rangle$ the Hall inner product.Character expansions and affine Jacobi-Trudi identities
We provide character expansions of certain specialisations of multiparameter Hall--Littlewood polynomials of types $\mathrm{B}_n$, $\mathrm{C}_n$, and $\mathrm{BC}_n$ for rectangular shapes.Posh Parking Spaces
Let $W$ be an irreducible complex reflection group with reflection representation $V$.Optimal large sieve for fixed order characters
Let $n \geq 3$.Beyond Liu's 0.382709 threshold for the union-closed sets conjecture
The union-closed sets conjecture asks whether every finite union-closed family containing a nonempty set has an element contained in at least half of its members.The twisted convolution identity and ghost $r$-SICs from finite quantum dilogarithms
Radchenko and Wheeler (RW) recently proved a finite pentagon relation for real quadratic special values of the modular quantum dilogarithm and used it to establish the rank-$1$ twisted convolution…A Memory-Magic Exchange Law in Streaming Clifford+T Compilation
A phase that reaches a fault-tolerant processor in additive pieces can be remembered until the last piece arrives, or executed on arrival: the first option costs classical memory carried across…Large-Scale Autonomous Discovery of Kissing Number Constructions
The kissing-number problem is a classical problem in discrete geometry whose exact solution is known in only a few dimensions.More than 83.69% of the zeros of the Riemann zeta function are distinct
The lower asymptotic proportion of distinct nontrivial zeros of the Riemann zeta function, counted with multiplicity, is at least $0.8369928814\ldots$.Duality for matrix space questions
We present a new proof of a classical theorem of Dieudonné: if a linear space of $n\times n$ matrices consists entirely of singular matrices, then its dimension is at most $n^2-n$.A New Upper Bound for the Turán Density of the Tetrahedron
We prove that the Turán density of the tetrahedron $K_4^{(3)}$ satisfies $π(K_4^{(3)}) \le 14993367693127837/26880000000000000 < 0.557789$, improving Baber's upper bound of $0.5615$ and closing…Lengths of Hodge characters in Fermat varieties
We revisit the Hodge conjecture for Fermat (and weighted Fermat) varieties.On the generation of multiplicative groups by small primes
Motivated by a question of Regev arising from his improved quantum factoring algorithm, we study how many small primes are needed to generate the group $({\mathbb Z}/q{\mathbb Z})^\times$ when each…Continuous Optimization for p-adic Models
We present the first method for native, continuous gradient descent for machine learning models with $p$-adic parameters.Inverse Baer deformations and finite simple skew braces of nilpotent type
Finite simple skew braces with non-abelian additive group remain largely unexplored.