相关论文: On the Landau-Siegel Zeros Conjecture

We give an example for the Kuznetsov-Shinder conjecture, with infinitely many non-isomorphic D-equivalent and L-equivalent varieties.

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

We use the Gromov-Witten invariants and a nonsqueezing theorem by the author to affirm a conjecture by P.Biran on the Lagrangian barriers.

In this paper, we present a proof of the Riemann hypothesis. We show that zeros of the Riemann zeta function should be on the line with the real value 1/2, in the region where the real part of complex variable is between 0 and 1.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We present a relative form of the Toponogov comparison theorem.

In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…

In this note, we prove Selberg's announced result on $r$-gaps between zeros of the Riemann zeta-function $\zeta$. Our proof uses a result on variations of $\arg\zeta$ by Tsang based on Selberg's method. The same result with explicit…

We find an elementary proof for Voiculescu's theorem on the polar decomposition of circular variables.

In this paper, we apply the ratio conjecture of $L$-functions to derive the lower order terms of the $1$-level density of the low-lying zeros of a family quadratic Hecke $L$-functions in the Gaussian field. Up to the first lower order term,…

Riemann numerically approximated at least three zeta zeros. According to Edwards, Riemann even took steps to verify that the lowest zero he computed was indeed the first zeta zero. This approach to verification is developed, improved, and…

In this note a far extension of the Banach fixed point theorem is proved.

Several results about the union-closed sets conjecture are presented.

We discuss various recent advances on weak forms of the Twin Prime Conjecture.

We study the distribution of prime numbers under the unlikely assumption that Siegel zeros exist. In particular we prove for \[ \sum_{n \leq X} \Lambda(n) \Lambda(\pm n+h) \] an asymptotic formula which holds uniformly for $h = O(X)$. Such…

We prove a conjecture due to Y. Last on Jacobi matrices.

In this paper, by making use of one of Chen's theorems and the method of mathematical analysis, we refine Edwards-Child's inequality and solve a conjecture posed by Liu.

We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

An observation on Hall-Littlewood polynomials.