相关论文: Thoughts on the Riemann hypothesis

Physics is a fertile environment for trying to solve some number theory problems. In particular, several tentative of linking the zeros of the Riemann-zeta function with physical phenomena were reported. In this work, the Riemann operator…

We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these…

Anthropic reasoning is a critical tool to understand probabilities, especially in a large universe or multiverse. According to anthropic reasoning, we should consider ourselves typical among members of a reference class that must include…

We investigate the degree to which human plausibility judgments of multiple-choice commonsense benchmark answers are subject to influence by (im)plausibility arguments for or against an answer, in particular, using rationales generated by…

L. de Branges proposed an approach to the Riemann hypothesis using certain positivity conditions. In this paper, the authors examine this approach and indicate its difficulty.

In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…

Since its beginnings in the 1940s, automated reasoning by computers has become a tool of ever growing importance in scientific research. So far, the rules underlying automated reasoning have mainly been formulated by humans, in the form of…

Discrete moments of the Riemann zeta function were studied by Gonek and Hejhal in the 1980's. They independently formulated a conjecture concerning the size of these moments. In 1999, Hughes, Keating, and O'Connell, by employing a random…

We discuss properties of recursive schemas related to McCarthy's ``91 function'' and to Takeuchi's triple recursion. Several theorems are proposed as interesting candidates for machine verification, and some intriguing open questions are…

This note is a critical examination of the argument of Frauchiger and Renner (Nature Communications 9:3711 (2018)), in which they claim to show that three reasonable assumptions about the use of quantum mechanics jointly lead to a…

The paper is partly a survey with historical background and references, partly provides the opportunity to put in print some unpublished early work, and partly has new results. A special case of relative categoricity is identified (almost…

In this paper we set up the theory of acid zeta function and ajoint acid zeta function, based on the theory, we point out a reason to doubt the truth of the Riemann hypothesis and also as a consequence, we give out some new RH equivalences.

Traditional approaches to non-monotonic reasoning fail to satisfy a number of plausible axioms for belief revision and suffer from conceptual difficulties as well. Recent work on ranked preferential models (RPMs) promises to overcome some…

The Frauchiger-Renner argument aims to show that `quantum theory cannot consistently describe the use of itself': in many-party settings where agents are themselves subject to quantum experiments, agents may make predictions that contradict…

A lengthy bibliography of books referring to special and/or general relativity is provided to give a background for discussions on the historical use of the concept of relativistic mass.

The hypothesis of the random flow of time is considered. To do this, the concepts of microscopic random time and macroscopic mean time, as well as random modular time are introduced. The possibilities of experimental verification of the…

Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most…

This article is a brief personal account of the past, present, and future of algorithmic randomness, emphasizing its role in inductive inference and artificial intelligence. It is written for a general audience interested in science and…

We prove that an innocent looking inequality implies the Riemann Hypothesis and show a way to approach this inequality through sums of Legendre symbols.

There has been a recent stimulus in the study of alternative theories of gravity lately, mostly triggered from combined motivation coming from cosmology/astrophysics and high energy physics. Among the proposed theories, one that has…