An analytic function and iterated integrals
Bruno Harris (1988)
Compositio Mathematica
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Displaying similar documents to “Convolution -series”
An analytic function and iterated integrals
Integral transforms of the Kontorovich-Lebedev convolution type.
Semyon B. Yakubovich (2003)
Collectanea Mathematica
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The reciprocal of the beta function and Whittaker functions
Eric Stade (1994)
Annales de l'institut Fourier
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In this paper we derive, using the Gauss summation theorem for hypergeometric series, a simple integral expression for the reciprocal of Euler’s beta function. This expression is similar in form to several well-known integrals for the beta function itself. We then apply our new formula to the study of Whittaker functions, which are special functions that arise in the Fourier theory for automorphic forms on the general linear group. Specifically, we deduce explicit integral...
On the order of vanishing of modular -functions at the critical point
Henryk Iwaniec (1990)
Journal de théorie des nombres de Bordeaux
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Hecke's functional equation and the average order of arithmetical functions
K Chandrasekharan, Raghavan Narasimhan (1961)
Acta Arithmetica
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Special values of twisted symmetric square -functions and the trace formula
Jeffrey Stopple (1996)
Compositio Mathematica
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L-functions and character sums for quadratic forms (II)
H. Stark (1969)
Acta Arithmetica
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On a semigroup of measures with irregular densities
Przemysław Gadziński (2000)
Colloquium Mathematicae
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We study the densities of the semigroup generated by the operator on the 3-dimensional Heisenberg group. We show that the 7th derivatives of the densities have a jump discontinuity. Outside the plane x=0 the densities are . We give explicit spectral decomposition of images of in representations.