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Journal of the London Mathematical Society Advance Access originally published online on May 9, 2008
Journal of the London Mathematical Society 2008 78(1):183-197; doi:10.1112/jlms/jdn021
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© 2008 London Mathematical Society

The Rankin–Selberg convolution for real analytic Cohen's Eisenstein series of half-integral weight

Yoshinori Mizuno

Max-Planck-Institut für Mathematik
Vivatsgasse 7
D-53111 Bonn
Germany

We give a meromorphic continuation and a functional equation for the Rankin–Selberg convolution of certain real analytic Eisenstein series of half-integral weight. Our result and method have several applications to the Koecher–Maass series associated with the real analytic Siegel–Eisenstein series.

Dedicated to Professor Tomoyoshi Ibukiyama on the occasion of his 60th birthday

2000 Mathematics Subject Classification 11F46 (primary), 11F37 (secondary).

Received April 24, 2007; revised January 22, 2008; published online May 9, 2008.


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