Results 121 to 130 of about 229 (136)

TRANSFORMATION FORMULAS FOR GENERALIZED DEDEKIND ETA FUNCTIONS

Bulletin of the London Mathematical Society, 2004
The author considers the generalized Dedekind eta functions \[ E_{g,h}(\tau)= q^{\frac12 B(g/N)}\cdot\prod^\infty_{n=1}(1 - \zeta^h q^{m-1+g/N})(1 - \zeta^-h)q^{m-g/N}). \] Here, \(N\) is a positive integer, \(g\) and \(h\) are real numbers which are not simultaneously multiples of \(N\), \(\zeta = e^{2\pi i/N}\), \(B(x) = x^2 - x + \frac16\), and \(q =
openaire   +1 more source

Values of the Dedekind Eta Function at Quadratic Irrationalities: Corrigendum

Canadian Journal of Mathematics, 2001
AbstractHabib Muzaffar of Carleton University has pointed out to the authors that in their paper [A] only the resultfollows from the prime ideal theorem with remainder for ideal classes, and not the stronger resultstated in Lemma 5.2. This necessitates changes in Sections 5 and 6 of [A].
van der Poorten, Alfred J., Williams, Kenneth S.   +1 more
openaire   +1 more source

Dedekind η-Function in Modern Research

Journal of Mathematical Sciences, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Ramanujan's Eisenstein series and powers of Dedekind's eta-function

Journal of the London Mathematical Society, 2007
The authors construct theta function identities that enable them to express certain theta functions in the form \(\eta^d(\tau)F(P, Q, R)\), where \(\eta(\tau)\) is the Dedekind eta function, and \(F(P, Q, R)\) is a polynomial in Ramanujan's Eisenstein series \(P\), \(Q\), \(R\).
Chan, H.H., Cooper, S., Toh, P.C.
openaire   +2 more sources

Dedekind η-function and indefinite quadratic forms

Functional Analysis and Its Applications, 1985
The author investigates some special theta series with the property \(\Theta (\tau)=\nu \eta^ d(\tau)\). Here \(\eta (\tau)\) is the Dedekind \(\eta\)-function, \(\nu\) is a constant. The author extends the method of the paper [\textit{A. G. van Asch}, Math. Ann.
openaire   +2 more sources

Modular Equations for the Rogers-Ramanujan Continued Fraction and the Dedekind Eta-Function

The Ramanujan Journal, 2001
For \(| q|
openaire   +2 more sources

Multiplicative Products of Dedekind η-Functions and Group Representations

Mathematical Notes, 2003
The present paper continues the author's investigations of metacyclic groups which began in the papers [1,2]. The author gives all metacyclic groups \(\langle a,b:a^m=e,b^s=e,b^{-1}ab=a^r\rangle\), where \(m=10,14,15,20,21,22\), such that the cusp forms associated with all elements of these groups by an exact representation are multiplicative \(\eta ...
openaire   +1 more source

Linear Congruences for Power Products of Dedekind η-Functions

Journal of the London Mathematical Society, 1989
A. O. L. Atkin has obtained Ramanujan type congruences for the coefficients of P(x) k, k a positive integer, where \(P(x)=\sum^{\infty}_{n=0}p(n)x\) n is the partition generating function. B. Gordon and K. Hughes proved a similar theorem for the coefficients of the integral powers of the theta function \(\theta (x)=1+2\sum^{\infty}_{n=1}x^{n^ 2 ...
openaire   +2 more sources

Dedekind $$\eta $$-function identities of level 6 and an approach towards colored partitions

Boletin De La Sociedad Matematica Mexicana, 2021
Shruthi, B R Srivatsa Kumar, Kumar B R Srivatsa   +2 more
exaly  

An integral of Dedekind An integral of Dedekind An integral of Dedekind An integral of Dedekind eta-functions in Ramanujans lost notebook

Journal für die reine und angewandte Mathematik (Crelles Journal), 2002
Bruce C. Berndt, Alexandru Zaharescu
openaire   +1 more source