Related papers: On Doubly Periodic Phases

The paper determines all meromorphic functions with finitely many zeros in the plane having the property that a linear differential polynomial in the function, of order at least 3 and with rational functions as coefficients, also has…

We consider Hamiltonian diffeomorphisms of the Euclidean space, generated by compactly supported time-dependent perturbations of hyperbolic quadratic forms. We prove that, under some natural assumptions, such a diffeomorphism must have…

Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = f(z+1) - f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f.

For a $C^{1}$ degree two latitude preserving endomorphism $f$ of the 2-sphere, we show that $f$ has $2^{n}$ periodic points.

The parabolic functions are introduced in analogy to the circular and hyperbolic cases. We discuss the relevant properties, the geometrical interpretation and touch on possible generalizations and their link with the modular elliptic…

We present a simple and effective method for representing periodic functions and enforcing exactly the periodic boundary conditions for solving differential equations with deep neural networks (DNN). The method stems from some simple…

We extend the notion of amoeba to holomorphic almost periodic functions in tube domains. In this setting, the order of a function in a connected component of the complement to its amoeba is just the mean motion of this function. We also…

The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus $3$ is described in terms of the gradient of it's sigma function. Solutions of corresponding families of polynomial dynamical systems in $\mathbb{C}^4$…

Let F and G be two families of meromorphic functions on a domain D, and let a, b and c be three distinct points in the extended complex plane. Let G be a normal family in D such that all limit functions of G are non-constant. If for each f…

The notions of almost periodicity in the sense of Weyl and Besicovitch of the order p are extended to holomorphic functions on a strip. We prove that the spaces of holomorphic almost periodic functions in the sense of Weyl for various…

The periods of the three-form on a Calabi-Yau manifold are found as solutions of the Picard-Fuchs equations; however, the toric varietal method leads to a generalized hypergeometric system of equations which has more solutions than just the…

We give an elementary characterization of rational functions among meromorphic functions in the complex plane.

In this paper we establish a close connection between three notions at- tached to a modular subgroup. Namely the set of weight two meromorphic modular forms, the set of equivariant functions on the upper half-plane commuting with the action…

The object of this paper is studying some properties of meromorphic functions which satisfy in the condition \[Re(zf(z)) > \alpha|z^2f'(z)+zf(z)| .\] Parallel results for some related classes are also obtained.

A continuous solution of an algebraic equation with holomorphic almost periodic coefficients is also almost periodic.

We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized…

A mathematical model is given for the occurrence of preferred orbits and orbital velocities in a Keplerian system. The result can be extended into energies and other properties of physical systems. The values given by the model fit closely…

We provide an effective method to compute multiplier ideals of meromorphic functions in dimension two. We also prove that meromorphic functions only have integer jumping numbers after reaching some threshold.

This paper is to characterize piecewise continuous almost periodic functions as the product of Bohr almost periodic functions and sequences. As an application, the result is used to discuss piecewise continuous almost periodic solutions of…

The standard twist of $L$-functions plays a fundamental role in the Selberg class theory. It is defined as an absolutely convergent Dirichlet series and admits meromorphic continuation beyond the half-plane of absolute convergence.…