Results 81 to 90 of about 114 (98)

Evaluation of some q-integrals in terms of the Dedekind eta function

Analysis (Germany), 2018
Abstract A q-integral is a definite integral of a function of q having an expansion in non-negative powers of q for {|q|<1} (q-series). In his book on hypergeometric series, N. J. Fine [N. J.
Greg Doyle, Kenneth S Williams
exaly   +2 more sources

Fourier coefficients of powers of the Dedekind eta function

Ramanujan Journal, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
, Florian Rupp, Neuhaüser Markus
exaly   +3 more sources

Some Algebraic Number Theory Estimates Based on the Dedekind Eta-Function

American Journal of Mathematics, 1956
Harvey Cohn
exaly   +2 more sources

Applications of Hecke Operator to Generalized Dedekind Eta Functions

AIP Conference Proceedings, 2009
The aim of this paper is to give relations between generalized Dedekind eta functions, theta functions, Dedekind sums, Hardy‐Berndt sums and Hecke operators.
Mehmet Acikgoz, Ismail Naci Cangul, Daeyeoul Kim, Yilmaz Simsek, Theodore E. Simos, George Psihoyios, Ch. Tsitouras   +6 more
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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
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Dedekind η-Function in Modern Research

Journal of Mathematical Sciences, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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.
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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.
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Modular Equations for the Rogers-Ramanujan Continued Fraction and the Dedekind Eta-Function

The Ramanujan Journal, 2001
For \(| q|
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