Proceedings of the Japan Academy, Series A, Mathematical Sciences

On Kaufhold’s Whittaker functions

Shinji Niwa

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In this paper we give an integral representation for a Whittaker function of an non holomorphic Eisenstein series which is a non holomorphic Sigel modular form of degree 2. Our integral representation is very useful to the theory of the theta lifting of automorphic forms.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 88, Number 7 (2012), 103-108.

First available in Project Euclid: 6 July 2012

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Primary: 11F27: Theta series; Weil representation; theta correspondences 11F37: Forms of half-integer weight; nonholomorphic modular forms 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms

Siegel modular theta correspondence generalized Whittaker functions


Niwa, Shinji. On Kaufhold’s Whittaker functions. Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), no. 7, 103--108. doi:10.3792/pjaa.88.103.

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  • W. N. Bailey, Generalized hypergeometric series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 32, Stechert-Hafner, Inc., New York, 1964.
  • I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, translated from the Russian, translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger, seventh edition, Elsevier/Academic Press, Amsterdam, 2007.
  • C. S. Herz, Bessel functions of matrix argument, Ann. of Math. (2) 61 (1955), 474–523.
  • G. Kaufhold, Dirichletsche Reihe mit Funktionalgleichung in der Theorie der Modulfunktion 2. Grades, Math. Ann. 137 (1959), 454–476.
  • S. Niwa, On generalized Whittaker functions on Siegel's upper half space of degree 2, Nagoya Math. J. 121 (1991), 171–184.
  • G. Shimura, Confluent hypergeometric functions on tube domains, Math. Ann. 260 (1982), no. 3, 269–302.