Add to ORKGAbstract. A new technique is described for explicitly evaluating quotients of the Dedekind eta function at quadratic integers. These evaluations do not make use of complex approximations but are found by an entirely ‘algebraic’ method. They are obtained by means of specialising certain modular equations related to Weber’s modular equations of ‘irrational type’. The technique works for a large class of eta quotients evaluated at points in an imaginary quadratic field with discriminant d ≡ 1 (mod 8). In particular, this method does place any restriction on the class number of the associated imaginary quadratic number field
The sum of divisors function σ(m) is defined by σ(m) = {∑d d∈ℕ d|m if m ∈ ℕ, 0 if m ∈ ℚ, m ∉ ℕ. Let ...
In his lost notebook, Ramanujan defined a parameter λn by a certain quotient of Dedekind eta-functio...
This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic ...
A technique is described for explicitly evaluating quotients of the Dedekind eta function at quadrat...
Abstract. We extend the methods of Van der Poorten and Chapman [7] for explicitly evaluating the Ded...
A generalised Weber function is given by $\w_N(z) = \eta(z/N)/\eta(z)$, where $\eta(z)$ is the Dedek...
ABSTRACT. Let η(z) denote the Dedekind eta function. Let ax2+ bxy+ cy2 be a positive-definite, primi...
We give an explicit formula for the Hauptmodul (eta(tau)/eta(13 tau))(2) of the level-13 Hecke modul...
Abstract. We describe the construction of a new type of modular equation for Weber functions. These ...
Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b2 - 4a...
Let n(z) (ϵ) denote the Dedekind eta function. We use a recent product- To-sum formula in conjunctio...
version finaleInternational audienceThe classical modular equations involve bivariate polynomials th...
We give an exposition of Heegner's and Siegel's proofs that there are exactly 9 imaginary quadratic ...
The absolute invariant J(z), of the modular group M arises in the theory of elliptic functions, (Whe...
We determine the conditions under which singular values of multiple $\eta$-quotients of square-free ...
The sum of divisors function σ(m) is defined by σ(m) = {∑d d∈ℕ d|m if m ∈ ℕ, 0 if m ∈ ℚ, m ∉ ℕ. Let ...
In his lost notebook, Ramanujan defined a parameter λn by a certain quotient of Dedekind eta-functio...
This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic ...
A technique is described for explicitly evaluating quotients of the Dedekind eta function at quadrat...
Abstract. We extend the methods of Van der Poorten and Chapman [7] for explicitly evaluating the Ded...
A generalised Weber function is given by $\w_N(z) = \eta(z/N)/\eta(z)$, where $\eta(z)$ is the Dedek...
ABSTRACT. Let η(z) denote the Dedekind eta function. Let ax2+ bxy+ cy2 be a positive-definite, primi...
We give an explicit formula for the Hauptmodul (eta(tau)/eta(13 tau))(2) of the level-13 Hecke modul...
Abstract. We describe the construction of a new type of modular equation for Weber functions. These ...
Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b2 - 4a...
Let n(z) (ϵ) denote the Dedekind eta function. We use a recent product- To-sum formula in conjunctio...
version finaleInternational audienceThe classical modular equations involve bivariate polynomials th...
We give an exposition of Heegner's and Siegel's proofs that there are exactly 9 imaginary quadratic ...
The absolute invariant J(z), of the modular group M arises in the theory of elliptic functions, (Whe...
We determine the conditions under which singular values of multiple $\eta$-quotients of square-free ...
The sum of divisors function σ(m) is defined by σ(m) = {∑d d∈ℕ d|m if m ∈ ℕ, 0 if m ∈ ℚ, m ∉ ℕ. Let ...
In his lost notebook, Ramanujan defined a parameter λn by a certain quotient of Dedekind eta-functio...
This monograph deals with products of Dedekind's eta function, with Hecke theta series on quadratic ...