Special values of derivatives of \(L\)-functions. (English) Zbl 0845.11021
Dilcher, Karl (ed.), Number theory. Fourth conference of the Canadian Number Theory Association, July 2-8, 1994, Dalhousie University, Halifax, Nova Scotia, Canada. Providence, RI: American Mathematical Society. CMS Conf. Proc. 15, 159-173 (1995).
Let \(f\) be a holomorphic newform of weight two for \(\Gamma_0(N)\) for which the corresponding \(L\)-function has a zero of odd order at \(s= 1\). The author expresses the special value of the derivative of the \(L\)-function at \(s= 1\) as a finite sum of additive one-cocylces for \(\Gamma_0(N)\) (Theorem 1). It generalizes Manin’s result, which concerned the expression of the special value of the \(L\)-function at \(s= 1\) as a finite sum of modular symbols [Yu. I. Manin, Izv. Akad. Nauk SSSR, Ser. Mat. 36, 19-66 (1972; Zbl 0243.14008)].
For the entire collection see [Zbl 0827.00036].
For the entire collection see [Zbl 0827.00036].
Reviewer: A.Dabrowski (Szczecin)
MSC:
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11G40 | \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture |
