Related papers: Identities about level 2 Eisenstein series

The classical Kronecker limit formula gives the constant term of the non-holomorphic Eisenstein series E(z,s) for SL(2,Z) at s=1 in terms of the Dedekind eta function. Here we compute the analagous formula for an Eisenstein series twisted…

We show that for fields that are of characteristic 0 or algebraically closed of characteristic greater than 5, that certain classes of Leibniz algebras are 2-recognizeable. These classes are solvable, strongly solvable and super solvable.…

In this paper, we study a class of double Lambert series and establish several identities and transformation relations for them. These formulae provide useful tools for reducing certain double Lambert series to single Lambert series. As…

A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…

A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated…

We review certain classes of iterated integrals that appear in the computation of Feynman integrals that involve elliptic functions. These functions generalise the well-known class of multiple polylogarithms to elliptic curves and are…

Let $\Gamma$ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane $\mathbb H$, and let $M = \Gamma \backslash \mathbb H$ be the associated finite volume hyperbolic Riemann surface. If $\gamma$ is parabolic, there…

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…

We give all possible holomorphic Eisenstein series on $\Gamma_0(p)$, of rational weights greater than $2$, and with multiplier systems the same as certain rational-weight eta-quotients at all cusps. We prove they are modular forms and give…

We study the product of Selberg Zeta function and hyperbolic Eisenstein series on a family of degenerating hyperbolic surfaces.

In the present paper, the authors introduce several new integral transforms including the Ln-transform, the L2n-transform and P2n-transform generalizations of the classical Laplace transform and the classical Stieltjes transform as…

We study a certain class of q-analogues of multiple zeta values, which appear in the Fourier expansion of multiple Eisenstein series. Studying their algebraic structure and their derivatives we propose conjectured explicit formulas for the…

This paper studies eight families of infinite series involving hyperbolic functions. Under some conditions, these series are linear combinations of derivatives of Eisenstein series. The paper gives a systematic method for computing the…

In this research article, we obtain few theta function identities of level ten employing Ramanujan's $_1 \psi_1$ summation formula. Using these identities, we derive a new modular equation of degree five. Further, we establish Eisenstein…

We investigate certain Eisenstein congruences, as predicted by Harder, for level p paramodular forms of genus 2. We use algebraic modular forms to generate new evidence for the conjecture. In doing this we see explicit computational…

Building of some isomorphic classes for noncanonical hypercomplex number systems o dimension 2 is described. In general case, such systems with specific constraints to structural constants can be isomorphic to complex, dual or double number…

We will characterize the Eisenstein series for O(2, n + 2) as a particular Hecke eigenform. As an application we show that it belongs to the associated Maa{\ss} space. If the underlying lattice is even and unimodular, this leads to an…

In this paper we consider the linear second order partial differential equation with non-constant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new…

This manuscript introduces a general multisection identity expressed equivalently in terms of infinite double products and/or infinite double series, from which several new product or summation identities involving special functions…

We carry out "Hecke summation" for the classical Eisenstein series $E_k$ in an adelic setting. The connection between classical and adelic functions is made by explicit calculations of local and global intertwining operators and Whittaker…