2007 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 completes the classification of torsion groups for elliptic curves over quintic number fields by identifying three specific sporadic groups—, , and —and demonstrating that 5 is the smallest degree where a non-cyclic sporadic torsion group occurs.
This paper proves that the partial sums of extended Rademacher random multiplicative functions exhibit arbitrarily large fluctuations exceeding almost surely, thereby affirmatively resolving Erdős Problem #1144 and establishing new almost sure lower bounds on the number of sign changes.
The paper establishes an asymptotic formula with a power-saving error term for a cubic moment of self-dual -functions, incorporating a small extra averaging over characters and confirming the main term conjectured by Conrey, Farmer, Keating, Rubinstein, and Snaith.
This paper establishes a quasipolynomial density bound for subsets of avoiding nontrivial similar copies of a nondegenerate -simplex, significantly improving upon previous polylogarithmic results by employing a novel density increment argument that combines the circle method with a new "cut operator" technique to decouple quadratic forms.
Motivated by the 2021 work of Chern and Tang on two-parameter modular functions, this paper constructs a three-parameter extension associated with the Rogers-Ramanujan continued fraction, deriving recursive eta-quotient representations that facilitate dissection formulas, including applications to overpartitions with restricted odd differences.
This paper resolves Serre's problem regarding the specialisation of Brauer group elements by proving the result for all cases where the number of variables is sufficiently large.
The paper demonstrates that for nonnegative integer coordinates with , the quadratic Bézier curve defined by , , and serves as an approximate envelope for line segments connecting Bézout coefficients of coprime numbers located in neighborhoods of and .
This paper argues that while a number field appears as a K(,1) from the Galois perspective, it does not from the Weil perspective, motivating the construction of the "Weil-Moore anima"—an object with the Weil group as its fundamental group but nontrivial higher homotopy groups—to achieve superior cohomological properties.
This paper extends the universality of the Cohen-Lenstra measure for cokernels of corners in random matrices over finite local rings from the uniform distribution to general i.i.d. distributions, provided the entry distribution is not concentrated on the translate of a subring or an ideal.
This paper establishes quantitative universality results for the cokernels of products of i.i.d. random matrices and associated flags over finite local rings, providing a quantitative analogue of prior findings by Huang, Nguyen, and Van Peski in the specific case of quotients of .