Results 111 to 120 of about 229 (136)
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The Dedekind eta function and D’Arcais-type polynomials
Research in Mathematical Sciences, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bernhard Heim +2 more
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Certain Modular Functions Similar to the Dedekind eta Function
Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg, 2002For any even and primitive Dirichlet character \(\psi\) the authors study properties of the function \[ \eta_\psi(z)=q^{-\tfrac 12 L(-1,\psi)} \prod^\infty_{n=1} (1-q^n)^{\psi(n)}, \] where \(q=\exp(2\pi iz)\) and \(L(s,\psi)\) is the Dirichlet \(L\)-function attached to \(\psi\).
Horie, T., Kanou, N.
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, 1976 In many applications of elliptic modular functions to number theory the eta function plays a central role.
Tom M. Apostol
core +3 more sources
Dedekind’s Eta Function and Modular Forms
Springer Monographs in Mathematics, 2011Throughout this monograph we use the notation $$e(z) = e^{2\pi iz}$$ where z is a complex number. We define the Dedekind eta function by the infinite product $$\eta(z) = e\bigl( {\tfrac{z}{24}}\bigr) \prod_{n=1}^{\infty} (1 - q^n) \qquad \mbox{with} \qquad q = e(z) .$$ (1.1) The product converges normally for q in the unit disc or ...
Gunter Kohler, Kohler Gunter
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On the Transformation Formula for the Dedekind Eta-Function
Developments in Mathematics, 2001A new simple proof of the transformation formula for the Dedekind eta-function is given. Some connections with certain infinite series are made.
Berndt Bruce C
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Evaluation of some q-integrals in terms of the Dedekind eta function
Analysis (Germany), 2018Abstract 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
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The Dedekind Eta-Function in Algebra and Number Theory: Old and New Problems
Journal of Mathematical Sciences, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
G V Voskresenskaya, Voskresenskaya G V
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An identity for the Dedekind eta-function involving two independent complex variables [PDF]
Bulletin of the London Mathematical Society, 2007 The authors prove a new identity for the Dedekind eta-function that involves third powers of the eta-function, with each of the two cubes being a function of a different complex ...
Berndt, Bruce C., Hart, William B.
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Vassiliev invariants and a strange identity related to the Dedekind eta-function
Topology, 2001 In this paper the “function” F(q)=∑n=0∞(1−q)(1−q2)⋯(1−qn) is studied. The series does not converge in any open set, but has well-defined values and derivatives of all orders when q is a root of unity.
Don Zagier
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Applications of Hecke Operator to Generalized Dedekind Eta Functions
AIP Conference Proceedings, 2009The 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 +6 more
openaire +4 more sources