Related papers: A Landen-type method for computation of Weierstras…
We apply classical invariant theory of binary forms to explicitly characterize isomorphism classes of hyperelliptic curves of small genus and, conversely, propose algorithms for reconstructing hyperelliptic models from given invariants. We…
We give a explicit computation of the pointed harmonic volumes of hyperelliptic curves with Weierstrass base points, which are paraphrased into a combinatorial formula.
Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of…
The Weierstrass representation for minimal surfaces in $\mathbb{R}^3$ provides a flexible method for constructing minimal surfaces of arbitrary genus. The topological limitations of minimal surfaces interfere with this providing a more…
We prove in this paper the global Lorentz estimate in term of fractional-maximal function for gradient of weak solutions to a class of p-Laplace elliptic equations containing a non-negative Schr\"odinger potential which belongs to reverse…
Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the…
A method for computation of the matrix Mittag-Leffler function is presented. The method is based on Jordan canonical form and implemented as a Matlab routine.
In this work we derive results concerning Elliptic Functions using as tools general formulas from previus work.
The study of the relation between the Weierstrass inducing formulae for constant mean curvature surfaces and the completely integrable euclidean nonlinear sigma-model suggests a connection among integrable sigma -models in a background and…
Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain new criteria equivalent to the Riemann hypothesis. Later, the same theorem was applied…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of $L$-functions. In particular, we find finite formulas for certain twisted central $L$-values of a family of elliptic curves…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
Classical hypergeometric functions are well-known to play an important role in arithmetic algebraic geometry. These functions offer solutions to ordinary differential equations, and special cases of such solutions are periods of…
In this paper, we study an iteration in defined by a diffeomorphism polynomial bounded. Semi invariant curves tend to curves with parametric Weierstrass-Mandelbrot's functions. So, self-similarity and fractal dimension are justified. We…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
This paper presents an algorithm to compute the value of the inverse Laplace transforms of rational functions with poles on arrangements of hyperplanes. As an application, we present an efficient computation of the partition function for…
We give a detailed account of the classical Van Kampen method for computing presentations of fundamental groups of complements of complex algebraic curves, and of a variant of this method, working with arbitrary projections (even with…
Index transforms with the product of the associated Legendre functions are introduced. Mapping properties are investigated in the Lebesgue spaces. Inversion formulas are proved. The results are applied to solve a boundary value problem in a…
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.