Related papers: On the Erdos-Fuchs theorem
We give a short proof of the convergence to the boundary of Riemann maps on varying domains. Our proof provides a uniform approach to several ad-hoc constructions that have recently appeared in the literature.
We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.
We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.
An overview of the recent developments in plurifine potential theory.
Several results about the union-closed sets conjecture are presented.
In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
We study the Erdos distance conjecture on the unit sphere in three dimensions using Fourier analytic methods.
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
We state and prove a function field analogue of Furusho for multiple zeta values.
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the…
We give a purely combinatorial proof for the infinitary van der Waerden's theorem.
Reconstruction theorem for the Moufang loops is proved.
We prove a second main theorem for elliptic projective planes.
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.
In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.
We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…
We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.