Abstract
The Dedekind eta-function is defined for any τ in the upper half-plane bywhere x = exp(2πiτ) and x1/24 = exp(2πiτ/24). By an eta-product we shall mean a functionwhere N ≥ 1 and eachrδ ∈ ℤ. In addition, we shall always assume that is an integer. Using the Legendre-Jacobi symbol (—), we define a Dirichlet character ∈ bywhen a is odd. If p is a prime for which ∈(p) ≠ 0and if F is a function with a Fourier seriesthen we define a Hecke operator Tp bywhereand
Publisher
Cambridge University Press (CUP)
Reference15 articles.
1. Modular Forms Whose Coefficients Possess Multiplicative Properties, II
2. Construction and application of a certain class of modular functions;Newman;Proc. London Math. Soc.,1956
3. Discontinuous Groups and Automorphic Functions
4. 3. Biagioli Anthony J. F. , Products of Powers of Transforms ofthe Dedekind Eta-function, thesis University of Wisconsin-Madison 1982.
5. Construction and Application of a Class of Modular Functions (II)†
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1. Eta Products and Theta Series Identities;Springer Monographs in Mathematics;2011
2. Multiplicative -quotients;Transactions of the American Mathematical Society;1996
3. The Classical Special Functions;The Mathematica GuideBook for Symbolics