Related papers: A proof of Smale's mean value conjecture

We consider Young (1985)'s characterization of the Shapley value, and give a new proof of this axiomatization. Moreover, as applications of the new proof, we show that Young (1985)'s axiomatization of the Shapley value works on various…

We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three. This will be a consequence of a sharp decoupling inequality for curves

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

This is an expository paper, giving a simplified proof of the cubic case of the main conjecture for Vinogradov's mean value theorem.

We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages of sequences with terms in a given finite set A. For every such set we completely characterize the numbers x ("intermediate values") with…

From Bombieri's mean value theorem one can deduce the prime number theorem being equivalent to the Riemann hypothesis and the least prime P(q) satisfying P(q)= O(q^2 [ln q]^32) in any arithmetic progressions with common difference q.

We prove mean comparison from a different perspective, where we introduce the concept of partial convolution.

A generalization of an inequality from IMO is proven.

We prove Simon's conjecture for 3-manifolds.

We provide a proof of the Borwein Conjecture using analytic methods.

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.

Here we outline a proof for the 4-dimensional smooth Poincare Conjecture.

Remarks on mathematical proof and the practice of mathematics.

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

We prove the Aharoni Berger Conjecture

In this note a general a Cauchy-type mean value theorem for the ratio of functional determinants is offered. It generalizes Cauchy's and Taylor's mean value theorems as well as other classical mean value theorems.

We prove a variation of Gronwall's lemma.

Let X1, ..., Xn be arbitrary non-negative independent random variables with respective expected values $\mu_{i}$ at most one. We sketch but do not prove an equivalent conjecture to Feige's Conjecture $\mathbb{P} \left( \sum_{i=1}^{n} X_{i}…

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

We obtain simple proofs of certain inequalites for bivariate means.