Related papers: Rhymes in primes

In recent work, G. E. Andrews and G. Simay prove a surprising relation involving parity palindromic compositions, and ask whether a combinatorial proof can be found. We extend their results to a more general class of compositions that are…

This paper is based on a talk given to motivated high school (and younger) students at a BAMA (Bay Area Math Adventure) event. Some of the methods used to study primes and twin primes are introduced.

This is a preface to Fields, Gravity, Strings and Beyond, a special issue collection of articles published in J. Phys. A in memory of Stanley Deser.

Let $\alpha>1$ be irrational and of finite type, $\beta\in\mathbb{R}$. In this paper, it is proved that for $R\geqslant13$ and any fixed $c\in(1,c_R)$, there exist infinitely many primes in the intersection of Beatty sequence…

We prove some general estimates for exponential sums over subsets of finite fields which are definable in the language of rings. This generalizes both the classical exponential sum estimates over varieties over finite fields due to Weil,…

We respond to some of the points made by Bennet and Blanck (2022) concerning a previous publication of ours (2021).

Researchers or students entering a emerging research area are particularly interested in what newly published papers will be most cited and which young researchers will become influential in the future, so that they can catch the most…

With the recent developments in large language models (LLMs) and their widespread availability through open source models and/or low-cost APIs, several exciting products and applications are emerging, many of which are in the field of STEM…

These are the preparatory notes for a Science & Music essay, "Playing by numbers", appeared in Nature 453 (2008) 988-989.

We present various new results on greedoids. We prove a theorem that generalizes an equivalent formulation of Edmonds' classic matroid polytope theorem to local forest greedoids -- a class of greedoids that contains matroids as well as…

Reward Model (RM) has demonstrated impressive potential for enhancing Large Language Models (LLM), as RM can serve as a proxy for human preferences, providing signals to guide LLMs' behavior in various tasks. In this paper, we provide a…

Sequence-to-sequence neural networks have recently achieved great success in abstractive summarization, especially through fine-tuning large pre-trained language models on the downstream dataset. These models are typically decoded with beam…

The Parry-Lord oral-formulaic theory was a breakthrough in understanding how oral narrative poetry is learned, composed, and transmitted by illiterate bards. In this paper, we provide an annotated reading of the mechanism underlying this…

The performance of large language models (LLMs) has recently improved to the point where models can perform well on many language tasks. We show here that--for the first time--the models can also generate valid metalinguistic analyses of…

This paper introduces the Primender sequence, a novel integer sequence defined by a hybrid rule that combines classical primality with modular digit-based conditions. Specifically, a number n is included in the sequence if it is prime or…

In this paper we present a new proof of a proposition presented in the article: Complexes of tournaments, directionality filtrations and persistent homology. This paper is part of Joaqu\'in Casta\~neda's undergraduate thesis.

We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize…

The concept of Mersenne primes is studied in real quadratic fields of class number 1. Computational results are given. The field $Q(\sqrt{2})$ is studied in detail with a focus on representing Mersenne primes in the form $x^{2}+7y^{2}$. It…

Language models are now capable of solving tasks that require dealing with long sequences consisting of hundreds of thousands of tokens. However, they often fail on tasks that require repetitive use of simple rules, even on sequences that…

This is a survey article on prime number races. Chebyshev noticed in the first half of the nineteenth century that for any given value of x, there always seem to be more primes of the form 4n+3 less than x then there are of the form 4n+1.…