p-adic distributions associated to Heegner points on modular curves
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.
scientific article; zbMATH DE number 3997979
scientific article