Related papers: On Bohr's equivalence theorem

We establish a correspondence between inverse sumset theorems (which can be viewed as classifications of approximate (abelian) groups) and inverse theorems for the Gowers norms (which can be viewed as classifications of approximate…

We prove several extensions of the Erdos-Fuchs theorem.

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply…

We prove some extensions of Andrews inequality.

We prove joint universality theorems on the half plane of absolute convergence for general classes of Dirichlet series with an Euler-product, where in addition to vertical shifts we also allow scaling. This generalizes our recent joint…

The note contains the proof of the uniqueness theorem for the inverse problem in the case of $n$-th order differential equation.

A proof is given of Rosenthal's \(\ell_1\) theorem.

We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of…

In this paper we point out that the proof of Kable's extension of the Wiener-Ikehara Tauberian theorem can be applied to the case where the Dirichlet series has a pole of order "$l / m$" without much modification (Kable proved the case $l =…

We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.

We give an alternative proof for the celebrated Bertrand's theorem as a corollary of the isochronicity of a certain family of centers.

We prove an infinitary version of the Brauer-Schur theorem.

We give a determination of the equivalence group of Euler-Bernoulli equation and of one of its generalizations, and thus derive some symmetry properties of this equation.

We extend Riemann's rearrangement theorem on conditionally convergent series of real numbers to multiple instead of simple sums.

For the Dirichlet series of the form $\displaystyle F(z,\omega)=\sum\nolimits_{k=0}^{+\infty} f_k(\omega)e^{z\lambda_k(\omega)} $ $ (z\in\mathbb{C},$ $\omega\in\Omega)$ with pairwise independent real exponents $(\lambda_k(\omega))$ on…

In this paper, we prove a converse theorem for half-integral weight modular forms assuming functional equations for $L$-series with additive twists. This result is an extension of Booker, Farmer, and Lee's result in [BFL22] to the…

We prove inversion of adjunction on log canonicity.