Let f be an even weight k>=2 modular form on a p-adically uniformizable Shimura curve for a suitable gamma 0-type level structure. Let K=Q be an imaginary quadratic field, satisfying Heegner conditions assuring that the sign appearing in the functional equation of the complex L-function of f/K is negative. We may attach to f, or rather a deformation of it, a p-adic L-function of the weight variable , also depending on K. Our main result is a formula relating the derivative of this p-adic L-function at k to the Abel-Jacobi images of so called Heegner cycles.
Heegner cycles and derivatives of p-adic L-functions / M.A. Seveso. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - 686:686(2014 Jan), pp. 111-148.
Heegner cycles and derivatives of p-adic L-functions
M.A. SevesoPrimo
2014
Abstract
Let f be an even weight k>=2 modular form on a p-adically uniformizable Shimura curve for a suitable gamma 0-type level structure. Let K=Q be an imaginary quadratic field, satisfying Heegner conditions assuring that the sign appearing in the functional equation of the complex L-function of f/K is negative. We may attach to f, or rather a deformation of it, a p-adic L-function of the weight variable , also depending on K. Our main result is a formula relating the derivative of this p-adic L-function at k to the Abel-Jacobi images of so called Heegner cycles.Pubblicazioni consigliate
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