Related papers: Computing Euler products and coefficients of class…
We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…
We provide a diagrammatic computation for the bilinear form, which is defined as the pairing between the (relative) cup products with every local coefficients and every integral homology 2-class of every links in the 3-sphere. As a…
In the present paper, we were mainly concerned with obtaining estimates for the general Taylor-Maclaurin coefficients for functions in a certain general subclass of analytic bi-univalent functions. For this purpose, we used the Faber…
In this note we will present how Euler's investigations on various different subjects lead to certain properties of the Legendre polynomials. More precisely, we will show that the generating function and the difference equation for the…
We describe two new algorithms for the efficient and rigorous computation of Dirichlet L-functions and their use to verify the Generalised Riemann Hypothesis for all such L-functions associated with primitive characters of modulus…
We generalize a method of Conrey and Ghosh (Invent. Math. 94 (1988)) to prove quantitative estimates for simple zeros of modular form L-functions of arbitrary conductor.
We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.
In this note we report on the conjectural identification of paramodular forms from Calabi-Yau motives of Hodge type (1, 1, 1, 1) of moderately low conductor. We calculate Euler factors from Calabi-Yau operators from the AESZ database by the…
The Dirichlet characters of reduced residue systems modulo m are tabulated for moduli m <= 195. The associated L-series are tabulated for m <= 14 and small positive integer argument s accurate to 10^(-50), their first derivatives for m <=…
We present several formulas for some specific multiple $L$-values of conductor four. This grew out from the study of zeta functions of level four of Arakawa-Kaneko type. Closely related is a new version of multiple poly-Euler numbers and we…
We introduce a new approach to quantize the Euler scheme of an $\mathbb{R}^d$-valued diffusion process. This method is based on a Markovian and componentwise product quantization and allows us, from a numerical point of view, to speak of…
A quick way to compute generating functions related to Pell-Padovan tetranacci numbers and classical sequences of recursions of order two is provided. Eight special instances can be computed at once.
An efficient procedure for the computation of the coefficients of Legendre expansions is here presented. We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of an Abel-type…
Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the…
We calculate the Euler characteristics of all of the Teichmuller curves in the moduli space of genus two Riemann surfaces which are generated by holomorphic one-forms with a single double zero. These curves can all be embedded in Hilbert…
The connection between multiple modular L-functions, as defined by Manin in [5], and modular iterated integrals was made explicit by Choie and Ihara [3] under the restrictive assumption that all modular forms involved have vanishing…
In this paper, we mainly show that Euler sums of generalized hyperharmonic numbers can be expressed in terms of linear combinations of the classical Euler sums.
Using the $\scr L$-invariant constructed in our previous paper we prove a Mazur-Tate-Teitelbaum style formula for derivatives of p-adic L-functions of elliptic modular forms at near central points. In the second version of the paper the…
We study the meromorphy of various Euler products of degree two attached to cusp forms including Ramanujan's $\Delta$-function.
We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.