Related papers: On the Erdos-Fuchs theorem

We proved three theorems of $S$-version of the mulyiplicity one.

In this paper, we will give an extension of Mok's theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.

We provide a short proof of the 1-dimensional flat chain conjecture.

Inspired by Chen-Wu-Wang (Math. Ann. 362: 305--319, 2015), we prove a Hartogs type extension theorem for plurisubharmonic functions across a compact complete pluripolar set, which is complementary to a classical theorem of Shiffman.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…

In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.

In the paper based on the question of Zhang and L\"{u}[15], we present one theorem which will improve and extend the results of Banerjee-Majumder [2] and a recent result of Li-Huang [9].

We establish an edge of the wedge theorem for the sheaf of holomorphic functions with exponential growth at infinity and construct the sheaf of Laplace hyperfunctions in several variables. We also study the fundamental properties of the…

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

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

We prove a variation of Gronwall's lemma.

We prove some general theorems for preserving Dependent Choice when taking symmetric extensions, some of which are unwritten folklore results. We apply these to various constructions to obtain various simple consistency proofs.

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

The paper presents a counterexample to the Hodge conjecture.

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

Roth's theorem is extended to finitely generated field extensions of $\Bbb Q$, using Moriwaki's framework for heights.

An extension of the Wigner-Araki-Yanase theorem to multiplicative conserved quantities is presented and approximate versions of the theorem are discussed.

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