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EVALUATION OF THE DEDEKIND ETA FUNCTION
, 2003
"... We extend the methods of Van der Poorten and Chapman [7] for explicitly evaluating the Dedekind eta function at quadratic irrationalities. Via Hecke Lseries we obtain evaluations in some new cases. Specifically we provide further evaluations at points in imaginary quadratic number fields with cla ..."
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We extend the methods of Van der Poorten and Chapman [7] for explicitly evaluating the Dedekind eta function at quadratic irrationalities. Via Hecke Lseries we obtain evaluations in some new cases. Specifically we provide further evaluations at points in imaginary quadratic number fields
REGULARITY OF THE ETA FUNCTION ON MANIFOLDS WITH CUSPS
, 901
"... Abstract. On a spin manifold with conformal cusps, we prove under an invertibility condition at infinity that the eta function of the twisted Dirac operator has at most simple poles and is regular at the origin. For hyperbolic manifolds of finite volume, the eta function of the Dirac operator twiste ..."
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Abstract. On a spin manifold with conformal cusps, we prove under an invertibility condition at infinity that the eta function of the twisted Dirac operator has at most simple poles and is regular at the origin. For hyperbolic manifolds of finite volume, the eta function of the Dirac operator
Residues Of The Eta Function For An Operator Of Dirac Type
 J. FUNCT ANAL
, 1992
"... We compute the asymptotics of Tr L 2 (P e \GammatP 2 ) where P is a first order operator of Dirac type; this is equivalent to evaluating the residues of the eta function. ..."
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Cited by 30 (6 self)
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We compute the asymptotics of Tr L 2 (P e \GammatP 2 ) where P is a first order operator of Dirac type; this is equivalent to evaluating the residues of the eta function.
ON THE SINGULARITIES OF THE ZETA AND ETA FUNCTIONS OF AN ELLIPTIC OPERATOR
"... Abstract. Let P be a selfadjoint elliptic operator of order m> 0 acting on the sections of a Hermitian vector bundle over a compact Riemannian manifold of dimension n. General arguments show that its zeta and eta functions may have poles only at points of the form s = k, where k ranges over all n ..."
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Cited by 1 (0 self)
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Abstract. Let P be a selfadjoint elliptic operator of order m> 0 acting on the sections of a Hermitian vector bundle over a compact Riemannian manifold of dimension n. General arguments show that its zeta and eta functions may have poles only at points of the form s = k, where k ranges over all
Values of the Dedekind eta function at quadratic irrationalities
 Canad. J. Math
, 1999
"... Abstract. Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b 2 − 4ac = d, a> 0, gcd(a, b, c) = 1. The value of η ( (b + √ d)/2a)  is determined explicitly, where η(z) is Dedekind’s eta function η(z) = e πiz/12 (1 − e m=1 ..."
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Cited by 6 (1 self)
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Abstract. Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b 2 − 4ac = d, a> 0, gcd(a, b, c) = 1. The value of η ( (b + √ d)/2a)  is determined explicitly, where η(z) is Dedekind’s eta function η(z) = e πiz/12 (1 − e m=1
Signature Defects and Eta Functions of Degenerations of Abelian Varieties
, 1995
"... . In this paper, we will calculate the eta functions for torus bundles over S 1 which arise from boundaries of degenerations of Abelian varieties when the local monodromies are unipotent or have finite orders. By using the special values of the eta functions, we obtain the signature defects for su ..."
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Cited by 2 (0 self)
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. In this paper, we will calculate the eta functions for torus bundles over S 1 which arise from boundaries of degenerations of Abelian varieties when the local monodromies are unipotent or have finite orders. By using the special values of the eta functions, we obtain the signature defects
AN IDENTITY FOR THE DEDEKIND ETAFUNCTION INVOLVING TWO INDEPENDENT COMPLEX VARIABLES
"... Recall that the Dedekind etafunction η(τ) is defined for q = e 2πiτ and τ ∈ H = {τ: Im τ> 0} by η(τ) = q 1/24 (q; q)∞, where ..."
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Cited by 3 (2 self)
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Recall that the Dedekind etafunction η(τ) is defined for q = e 2πiτ and τ ∈ H = {τ: Im τ> 0} by η(τ) = q 1/24 (q; q)∞, where
Zeta and eta functions for AtiyahPatodiSinger operators
 J. Geom. Anal
, 1996
"... 1The zeta function of a Laplacian ∆ is ζ(∆, s) = trace(∆−s), where ∆−s is taken to be zero in the nullspace of ∆. Minakshisundaram and Pleijel [MP] showed that for the Laplacian on a compact manifoldX with empty boundary, the zeta function has a meromorphic extension to the complex ..."
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Cited by 24 (3 self)
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1The zeta function of a Laplacian ∆ is ζ(∆, s) = trace(∆−s), where ∆−s is taken to be zero in the nullspace of ∆. Minakshisundaram and Pleijel [MP] showed that for the Laplacian on a compact manifoldX with empty boundary, the zeta function has a meromorphic extension to the complex
Results 1  10
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26,881