相关论文: On the Landau-Siegel Zeros Conjecture

The classical Brauer-Siegel conjecture describes the asymptotic behaviour of the product of the class number and the regulator in families of number fields. All known cases of the conjecture rely on reducing the problem, via group theoretic…

This note is an exposition of the proof of Thom's conjecture by Kronheimer and Mrowka, using the new Seiberg-Witten invariants.

We give a new proof of Carlitz-Wan's conjecture, previously proved by Lenstra (1995).Our proofs are natural and intuitive, and shed new insights into the study of exceptional polynomials.

In this paper we prove the Zariski-Lipman conjecture for log canonical spaces.

In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.

We give a new elementary proof of Landau's Prime Ideal Theorem. The proof is an extension of Richter's proof of the Prime Number Theorem. The main result contains other results related to the equidistribution of the prime ideal counting…

We prove a local version of the Mazur-Ulam theorem.

We prove Burkholder inequality using Bregman divergence.

We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the semiampleness in some elementary cases.

We prove Landen's transformation by a direct elementary transformation of infinite series

We prove that the Lalescu sequence is monotonically decreasing.

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

In this paper, we give a survey of the recent develpoments of the DDVV conjecture.

We survey on the recent progress toward mirror symmetry between Landau-Ginzburg models.

We prove under some assumptions that the Tate conjecture holds for products of Fermat varieties of different degrees.

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.

Landau damping is calculated using real variables, clarifying the physical mechanism.

We prove in this paper the Ax-Lindemann-Weierstrass theorem for all mixed Shimura varieties and discuss the lower bounds for Galois orbits of special points of mixed Shimura varieties. In particular we reprove a result of Silverberg in a…