Related papers: Algorithms for Algebraic and Arithmetic Attributes…
We propose hypergeometric constructions of simultaneous approximations to polylogarithms. These approximations suit for computing the values of polylogarithms and satisfy 4-term Apery-like (polynomial) recursions.
Let $\cp:=(P_1,...,P_s)$ be a given family of $n$-variate polynomials with integer coefficients and suppose that the degrees and logarithmic heights of these polynomials are bounded by $d$ and $h$, respectively. Suppose furthermore that for…
For primes p congruent to 1 mod 12, we present an explicit relation between the traces of Frobenius on a family of elliptic curves with j-invariant 1728/t and values of a particular 2F1-hypergeometric function over F_p. Additionally, we…
In his Ph. D. thesis, C. Lehr offers an algorithm which gives the stable model for p-cyclic covers of the projective line over a p-adic field under the conditions that the branch locus whose cardinal is m+1 has the so called equidistant…
In different areas of discrete mathematics, a certain type of polynomials, having coefficients in a field K of finite characteristic, has been considered. The form and the degree of these polynomials, here called projective, are simply…
Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…
We continue our study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we apply the approach of obtaining iteratated solutions to…
Cohomology operations (including the cohomology ring) of a geometric object are finer algebraic invariants than the homology of it. In the literature, there exist various algorithms for computing the homology groups of simplicial complexes…
A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…
An algorithm computing the restriction of a holonomic D-module to a linear subspace was given by T.Oaku in 1997. We consider a problem of computing the restriction for a given holonomic D-module with parameters. We will give a partial…
It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions…
We obtain an algorithm computing explicitly the values of the non solvable spectral radii of convergence of the solutions of a differential module over a point of type 2, 3 or 4 of the Berkovich affine line.
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
We introduce the notion of "hypergeometric" polynomials with respect to Newtonian bases. These polynomials are eigenfunctions ($L P_n(x) = \lambda_n P_n(x)$) of some abstract operator $L$ which is 2-diagonal in the Newtonian basis…
The main aim of this article is to establish several $p$-numerical radius inequalities via the $(f,g)$-Aluthge transform of Hilbert space operators and operator matrices. Furthermore, various classical numerical radius and norm inequalities…
In this note, basing on a certain functional equation of the dilogarithm function, we establish nontrivial lower bounds for the $p$-adic valuation (where $p$ is a given prime number) of some type of rational numbers involving harmonic…
Continued fractions have been long studied due to their strong properties, such as rational approximation. In this extent, their arithmetic over real numbers has represented an intriguing problem throughout the years. In this paper, we…
In the first paper of this sequence, we provided an explicit hypergeometric modularity method by combining different techniques from the classical, $p$-adic, and finite field settings. In this article, we explore an application of this…
An analogue of the Gauss-Lucas theorem for polynomials over the algebraic closure $\mathbb C_p$ of the field of $p$-adic numbers is considered.
We prove a general formula for the $p$-adic heights of Heegner points on modular abelian varieties with potentially ordinary (good or semistable) reduction at the primes above $p$. The formula is in terms of the cyclotomic derivative of a…