Related papers: On the Erdos-Fuchs theorem
We discuss five ways of proving Chernoff's bound and show how they lead to different extensions of the basic bound.
We calculate extensions between certain irreducible admissible representations of p-adic groups.
This is a revised version of Sh:430, section 6.
We give an elementary proof to Hasse theorem.
We revisit Ahlfors theory of covering surfaces thanks to Stokes theorem.
We prove extension results for meromorphic functions by combining the Kohn-Rossi extension theorems with Andreotti's theory on the algebraic and analytic dependence of meromorphic functions on pseudoconcave manifolds. Versions of Kohn-Rossi…
We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.
We prove the constructive version of Birkhoff's ergodic theorem following Vyugin but trying to separate and state explicitly the combinatorial statement on which this proof is based. We pose some questions related to this statement (and the…
We improve the previuosly known bound for some vertex Folkman numbers.
We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.
One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.
Remarks on the life and work of Paul Erdos.
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
We establish some new theorems on pentagon and pentagram.
We prove Faltings Finiteness Theorem using Rieffel's classification of the noncommutative tori.
We give four new proofs of the directed version of Brook's Theorem and an NP-completeness result.
We give a stack-theoretic proof for some results on families of hyperelliptic curves.
We give a direct proof of the Ohsawa-Takegoshi by solving directly the d-bar equation.
We prove Burkholder inequality using Bregman divergence.
We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.