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Character sums and small eigenvalues for Г0(p)

Published online by Cambridge University Press:  18 May 2009

Henryk Iwaniec
Henryk Iwaniec
Affiliation:
Polish Academy of Sciences, Mathematics Institute, Ul. Sniadeckich 8, (00-950) Warsaw, Poland
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Let Δ denote the Laplace operator acting on the space L2(Г/H) of automorphic functions with respect to a congruence group Г, square integrable over the fundamental domain F=Г/H. It is known that Δ has a point spectrum

with (Weyl's law)

and it has a purely continuous spectrum on [¼,∞) of finite multiplicity equal to the number of inequivalent cusps. The eigenpacket of the continuous spectrum is formed by the Eisenstein series Ea(z, s) on s = ½+it where a ranges over inequivalent cusps. The eigenfunctions ui(z) with positive eigenvalues are Maass cusp forms.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 27 , October 1985 , pp. 99 - 116
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

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