p-adic distributions associated to Heegner points on modular curves
type: Item
instance of: scholarly article
title: p-adic distributions associated to Heegner points on modular curves
zbMATH Open document ID: 0616.14024
DOI: 10.1007/BF01162249
author: Winfried Kohnen
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173847
review text: Let p be a prime number, let \(K_{\infty}\) be the anticyclotomic \({\mathbb{Z}}_ p\)-extension of a given imaginary quadratic field K, and let f be a normalized newform of \(weight^ 2\) and prime-to-p level. The author constructs a p-adic distribution on \(Gal(K_{\infty}/K)\) with values in the \({\mathbb{C}}_ p\)-vector space generated by the Heegner points in the \(K_{\infty}\)-rational points of the abelian variety associated to f. He then studies its Mellin-Mazur transform, and computes its critical values at certain characters of finite order. As in previous work of \textit{B. Mazur} [Proc. Int. Congr. Math., Warszawa 1983, Vol. 1, 185-211 (1984; Zbl 0597.14023)] and \textit{P. Schneider}, the construction relies on the universal norm property of Heegner points. These results should be compared to \textit{B. Perrin-Riou}'s computation of derivatives of p-adic L-functions [C. R. Acad. Sci., Paris, Sér. I 303, 165-168 (1986)] making use of Iwasawa theory.
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 11S40
Mathematics Subject Classification ID: 11F12
zbMATH DE Number: 3997979
zbMATH Keywords: modular curve
zbMATH Keywords: p-adic distribution
zbMATH Keywords: Heegner points
zbMATH Keywords: rational points
zbMATH Keywords: Mellin-Mazur transform
reviewed by: Daniel Bertrand
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3997979