Related papers: Malle's conjecture for fair counting functions

We describe a rational, but low resolution model of probability.

Let $\lambda$ denote the Liouville function. We show that the logarithmic mean of $\lambda(\lfloor \alpha_1n\rfloor)\lambda(\lfloor \alpha_2n\rfloor)$ is $0$ whenever $\alpha_1,\alpha_2$ are positive reals with $\alpha_1/\alpha_2$…

In this paper, a simple explanation for the Goldbach Conjecture is given. We have shown that the probability of violating the conjecture not only for the prime numbers, but also for any subset of natural numbers whose distribution is…

A proof of Smale's mean value conjecture from 1981 is given.

We give a counterexample of Morrison's cone conjecture for a strict Calabi-Yau threefold.

Let $\Omega\subset \mathbb{R}^d$ be a set of finite measure. The periodic tiling conjecture suggests that if $\Omega$ tiles $\mathbb{R}^d$ by translations then it admits at least one periodic tiling. Fuglede's conjecture suggests that…

We prove that there is no non-trivial integral positive solution to the generalized Fermat equation.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains. The same…

The article provides a counterexample to a conjecture by Blocki-Zwonek.

We construct an entire function $f$ with only three singular values whose order of growth can change under a quasiconformal equivalence. This is a counterexample to the Order Conjecture in the Speiser class ${\mathcal S}$ of entire…

In this paper, we prove a conjecture of Schnell in the surface case.

We give a reformulation of the Lehmer conjecture about algebraic integers in terms of a simple counting problem modulo p.

This somewhat unusual proof for the fact that the reals are uncountable, which is adapted from one of Bourbaki's proofs in "Fonctions d'une variable reelle", may be of some interest.

In the experimental verification of Bell's inequalities in real photonic experiments, it is generally believed that the so-called fair sampling assumption (which means that a small fraction of results provide a fair statistical sample) has…

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

Using predictions in mirror symmetry, C\u{a}ld\u{a}raru, He, and Huang recently formulated a "Moonshine Conjecture at Landau-Ginzburg points" for Klein's modular $j$-function at $j=0$ and $j=1728.$ The conjecture asserts that the…

First a few reformulations of Frankl's conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to…

We investigate Sarnak's conjecture on the M\"obius function in the special case when the test function is the indicator of the set of integers for which a real additive function assumes a given value.

In this paper, we investigate the Mill's ratio estimation problem and get two new inequalities. Compared to the well known results obtained by Gordon, they becomes tighter. Furthermore, we also discuss the inverse Q-function approximation…