相关论文: A proof of Kummer's theorem

By Rabinowitsch' trick Hilbert's Nullstellensatz follows from the weak Nullstellensatz (Rabinowitsch 1929). The weak version can be shown with elimination theory. Hilbert's original proof is also based on successive elimination. Lasker…

We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.

In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.

When it comes to partial numerical verification of the Riemann Hypothesis, one crucial part is to verify the completeness of a list of pre-computed zeros. Turing developed such a method, based on an explicit version of a theorem of…

In this paper, we find a new recurrence formula fo the Euler zeta functions.

We refine a recent heuristic developed by Keating and the second author. Our improvement leads to a new integral expression for the conjectured asymptotic formula for shifted moments of the Riemann zeta-function. This expression is…

Wigner's theorem asserts that any symmetry of a quantum system is unitary or antiunitary. In this short note we give two proofs based on the geometry of the Fubini-Study metric.

A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-like proof involving just two observers. On one hand, this new approach allows us to derive…

We provide an alternative constructive proof of the Asymmetric Lov\'asz Local Lemma. Our proof uses the classic algorithmic framework of Moser and the analysis introduced by Giotis, Kirousis, Psaromiligkos, and Thilikos in "On the…

We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.

Two proofs of a weighted weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for multilinear Calder\'on-Zygmund operators are given. The ideas are motivated by different proofs of the classical weak-type $(1,1)$ estimate for…

We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…

We prove by an elementary method the Riemann hypothesis for the local Euler factor of the zeta function of quadratic orders.

We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras called here…

A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…

A lemma stated by Ke Li in [arXiv:1208.1400] has been used in e.g. [arXiv:1510.04682,arXiv:1706.04590,arXiv:1612.01464,arXiv:1308.6503,arXiv:1602.08898] for various tasks in quantum hypothesis testing, data compression with quantum side…

This article will prove a theorem for the existence of k-factor for k>1 ,and present an efficient algorithm for computing k-factor for all values of k based on this theorem.

We investigate Wiener's Tauberian theorem from the perspective of limit functions, which results in several new versions of the Tauberian theorem. Based on this, we formulate and prove analogous Tauberian theorems for operators in the sense…