Heegner points, cycles and Maass forms

Svetlana Katok, Peter Sarnak

Research output: Contribution to journalArticle

81 Citations (Scopus)

Abstract

We derive for Hecke-Maass cusp forms on the full modular group a relation between the sum of the form at Heegner points (and integrals over Heegner cycles) and the product of two Fourier coefficients of a corresponding form of half-integral weight. Specializing to certain cycles we obtain the nonnegativity of the L-function of such a form at the center of the critical strip. These results generalize similar formulae known for holomorphic forms.

Original languageEnglish (US)
Pages (from-to)193-227
Number of pages35
JournalIsrael Journal of Mathematics
Volume84
Issue number1-2
DOIs
StatePublished - Feb 1 1993

Fingerprint

Cycle
Cusp Form
Modular Group
Nonnegativity
Fourier coefficients
L-function
Strip
Generalise
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Katok, Svetlana ; Sarnak, Peter. / Heegner points, cycles and Maass forms. In: Israel Journal of Mathematics. 1993 ; Vol. 84, No. 1-2. pp. 193-227.
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Heegner points, cycles and Maass forms. / Katok, Svetlana; Sarnak, Peter.

In: Israel Journal of Mathematics, Vol. 84, No. 1-2, 01.02.1993, p. 193-227.

Research output: Contribution to journalArticle

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