Related papers: Recent advances on Kawaguchi-Silverman conjecture

According to some discussions based on syllogism, we present results on the binary Goldbach conjecture in three categories: results that are weaker than the Goldbach conjecture, sufficient conditions for the Goldbach conjecture, and results…

We study the main open parts of the Kawaguchi--Silverman Conjecture, asserting that for a birational self-map $f$ of a smooth projective variety $X$ defined over $\overline{\mathbb Q}$, the arithmetic degree $\alpha_f(x)$ exists and…

We survey some old and new results on strong variants of Chang's Conjecture and related topics.

The more recent paper "Generic strange duality for K3 surfaces" by the authors contains stronger results.

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

We survey recent developments on generalizing the Gross--Zagier formula to high dimensional Shimura varieties, with an emphasis on the Arithmetic Gan--Gross--Prasad conjecture and the relative trace formula approach.

We give some results and conjectures about recurrence relations for certain sequences of binomial sums.

As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…

An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.

This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects

We review recent progress in the studies of left handed materials.

A proof of Sendov's conjecture is given.

We improve the previuosly known bound for some vertex Folkman numbers.

This brief comment reflects on the historical and current uses of the term "snowball sampling."

In this article, we discuss and survey the recent progress towards the Schottky problem, and make some comments on the relations between the Andr{\'e}-Oort conjecture, Okounkov convex bodies, Coleman's conjecture, stable modular forms,…

This survey deals with the construction of a category of spectral triples that is compatible with the Kasparov product in $KK$-theory. These notes serve as an intuitive guide to these results, avoiding the necessary technical proofs. We…

I discuss recent developments in the theoretical study of Higgs search at LHC.

We present some old and new results on dispersive estimates for Schroedinger equations.

We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper of the authors(arXiv:math.NT/0605563).

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.