Related papers: A proof of Smale's mean value conjecture
Various forms of Mean Value Theorems are available in the literature. If we use Flett's Mean Value Theorem in Extended Generalized Mean Value Theorem then what would the new theorem look like. A sincere effort is done to develop this…
We prove the validity of the strong version of the union of uniform closed balls conjecture, formulated in 2011 as [4, Conjecture 2.5], in the plane.
In this article, we derive an explicit formula for computing confidence interval for the mean of a bounded random variable. Moreover, we have developed multistage point estimation methods for estimating the mean value with prescribed…
We prove Malle's conjecture for $G \times A$, with $G=S_3, S_4, S_5$ and $A$ an abelian group. This builds upon work of the fourth author, who proved this result with restrictions on the primes dividing $A$.
In this paper, we proved the normal scalar curvature conjecture and the Bottcher-Wenzel conjecture.
In 1987, Alzer posed a conjecture on generalized logarithmic mean, which was introduced by Stolarsky in 1975. To prove Alzer's conjecture, Lou posed a conjecture on generalized inverse harmonic mean in 1995. By proving Lou's conjecture, the…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
In this paper, we prove a few lemmas concerning Fibonacci numbers modulo primes and provide a few statements that are equivalent to Wall-Sun-Sun Prime Conjecture. Further, we investigate the conjecture through heuristic arguments and…
The aim of this note is a proof of a recent conjecture of Kellner concerning the number of distinct prime factors of a particular product of primes. The proof uses profound results from analytic number theory, such as Granville-Ramar\'{e}'s…
Assuming some pointwise estimates on certain Weyl's sum, we prove the sharp estimates of the mean value associated to the following exponential sum $$ \sum_{n=1}^N e^{2\pi i tn^d +2\pi i xn}\,. $$
The article presents the proof of Casas-Alvero conjecture.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…
We propose a framework to prove Malle's conjecture for the compositum of two number fields based on proven results of Malle's conjecture and good uniformity estimates. Using this method we can prove Malle's conjecture for $S_n\times A$ over…
By doing a slight change to a beautiful and widely unknown argument by E. L. Stark [E. L. Stark, Application of a Mean Value Theorem for Integrals to Series Summation, Amer. Math. Monthly 85 (1978) 481--483.] we get a candidate to be…
In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
We give a new proof of the Smale conjecture for $\mathbb{RP}^3$ and all lens spaces using minimal surfaces and min-max theory. For $\mathbb{RP}^3$, the conjecture was first proved in 2019 by Bamler-Kleiner using Ricci flow.
We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes. The latter have applications to…