1613 papers
The "Math — Nt" category explores the fascinating world of number theory, where mathematicians investigate the deep properties and relationships of integers. This field delves into questions about prime numbers, divisibility, and the patterns that underpin our numerical universe, often revealing surprising connections to cryptography and computer science. While these concepts can seem abstract, they form the bedrock of modern digital security and pure mathematical thought.
At Gist.Science, we ensure these complex discoveries are accessible to everyone. We process every new preprint in this category directly from arXiv, transforming dense academic papers into clear, plain-language explanations alongside detailed technical summaries. This dual approach allows both curious beginners and seasoned researchers to grasp the latest breakthroughs without getting lost in the jargon.
Below are the latest number theory papers we have summarized from arXiv, ready for you to explore.
This paper provides an elementary characterization of all sixteen possible Galois groups of the irreducible polynomial over , demonstrating that the group is uniquely determined by the Galois groups of the associated polynomials and along with checking whether at most two specific expressions in and are rational squares.
This paper investigates the distribution of shapes in pure quartic number fields , proving that these shapes are confined to ten specific torus orbits determined by and governed by a product of continuous and discrete measures, thereby providing a non-generic limiting distribution that challenges previous assumptions about shape distributions in fixed-degree number field families.
Assuming the four exponentials conjecture is not required, this paper proves Hansel and Safer's conjecture that any subset of Gaussian integers recognizable in two multiplicatively independent bases (where at least one is not a root of an integer) must be eventually periodic, thereby generalizing the Cobham-Semenov theorem to Gaussian numerations.
This paper establishes a framework for defining difference operators on general elliptic lattices that preserve the degree of rational functions, thereby constructing first and second-order difference equations with rational solutions exhibiting orthogonality and biorthogonality properties up to the elliptic hypergeometric case.
This paper demonstrates how the theory of Lubin-Tate -modules can be used to determine the maximal abelian extension of a finite extension of .
This paper establishes upper and lower bounds for the maximum cardinality of -sets (Sidon sets with -separated sumsets) contained within the integer interval .
This paper proves that the smallest set of positive integers containing 2 and 3 and closed under the operation $ab-1$ for distinct elements has a positive lower density, thereby resolving a long-standing problem posed by Erdős and attributed to Hofstadter.
This paper presents the first non-trivial bound on the number of binomial coefficients coprime to 6, addressing a long-standing gap in understanding exceptional sets for integers with at least two distinct prime factors.
This paper establishes a bound for the short second moment of -functions associated with holomorphic cusp forms for over intervals of length (where ) using the trivial delta method combined with a conductor lowering technique.
This paper establishes generic equidistribution for semiabelian varieties equipped with monocritical and arithmetically T-effective toric metrics by isolating and reinterpreting K{ü}hne's asymptotic estimates as compression path estimates, thereby extending Bogomolov-type results beyond the quasi-canonical range.