Related papers: On Bohr's equivalence theorem

Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In…

The following extension of Bohr's theorem is established: If a somewhere convergent Dirichlet series $f$ has an analytic continuation to the half-plane $\mathbb{C}_\theta = \{s = \sigma+it\,:\, \sigma>\theta\}$ that maps $\mathbb{C}_\theta$…

We prove an analogue of the Lagrange Inversion Theorem for Dirichlet series. The proof is based on studying properties of Dirichlet convolution polynomials, which are analogues of convolution polynomials introduced by Knuth in [4].

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.

We prove Burkholder inequality using Bregman divergence.

The paper presents a counterexample to the Hodge conjecture.

We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one. We also give an application of natural boundaries in determining asymptotic results.

We survey the classical results of the Dirichlet Approximation Theorem.

The Dirichlet divisor problem is used as a model to give a conjecture concerning the conditional convergence of the Dirichlet series of an L-function.

We give a transform of convergent trigonometric series into equivalent convergent series and sufficient conditions for the transformed series to converge faster than the original one.

Given two arbitrary almost periodic functions with associated Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip $V$, where both functions assume the same…

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

In this paper, we would like to propose a fundamental question about a higher dimensional analogue of Dirichlet's unit theorem. We also give a partial answer to the question as an application of the arithmetic Hodge index theorem.

The main aim of this paper is to prove a generalization of the classical Bohr theorem and as an application, we obtain a counterpart of Bohr theorem for the generalized Ces\'aro operator.

In this paper we prove the Bohr Theorem for slice regular functions. Following the historical path that led to the proof of the classical Bohr Theorem, we also extend the Borel-Carath\'eodory Theorem to the new setting.

We present quantitative versions of Bohr's theorem on general Dirichlet series $D=\sum a_{n} e^{-\lambda_{n}s}$ assuming different assumptions on the frequency $\lambda:=(\lambda_{n})$, including the conditions introduced by Bohr and…

Associated to a newform $f(z)$ is a Dirichlet series $L_f(s)$ with functional equation and Euler product. Hecke showed that if the Dirichlet series $F(s)$ has a functional equation of a particular form, then $F(s)=L_f(s)$ for some…

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.