Heegner Points and L-Series of Automorphic Cusp Forms of Drinfeld Type

@inproceedings{Rck2000HeegnerPA,
  title={Heegner Points and L-Series of Automorphic Cusp Forms of Drinfeld Type},
  author={Hans-Georg R{\"u}ck and Ulrich Tipp},
  year={2000}
}
In their famous article [Gr-Za], Gross and Zagier proved a formula relating heights of Heegner points on modular curves and derivatives of L-series of cusp forms. We prove the function field analogue of this formula. The classical modular curves parametrizing isogenies of elliptic curves are now replaced by Drinfeld modular curves dealing with isogenies of Drinfeld modules. Cusp forms on the classical upper half plane are replaced by harmonic functions on the edges of a Bruhat-Tits tree. As a… CONTINUE READING
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Drinfeld modular curves

  • E.-U. Gekeler
  • LNM 1231,
  • 1986

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