Plus/minus \(p\)-adic \(L\)-functions for Hilbert modular forms. (English) Zbl 1302.11088
The main idea, which is not that different from Pollack’s idea [R. Pollack, Duke Math. J. 118, No. 3, 523–558 (2003; Zbl 1074.11061)], is to analyse the growth conditions of the reviewer’s \(p\)-adic \(L\)-functions for Hilbert modular forms for different choices at \(p\)-Frobenius roots [Ann. Inst. Fourier 44, No. 4, 1025–1041 (1994; Zbl 0808.11035)].
Let us note that B. Zhang [J. Number Theory 131, No. 3, 419–439 (2011; Zbl 1219.11135)] also used the \(p\)-adic \(L\)-function constructed by the reviewer to give plus/minus \(p\)-adic \(L\)-functions for Hilbert modular forms.
Let us note that B. Zhang [J. Number Theory 131, No. 3, 419–439 (2011; Zbl 1219.11135)] also used the \(p\)-adic \(L\)-function constructed by the reviewer to give plus/minus \(p\)-adic \(L\)-functions for Hilbert modular forms.
Reviewer: Andrzej Dąbrowski (Szczecin)
MSC:
| 11R23 | Iwasawa theory |
| 11F67 | Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols |
| 11F41 | Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces |
| 11S40 | Zeta functions and \(L\)-functions |
Keywords:
Hilbert modular forms; \(p\)-adic \(L\)-functions at supersingular primes; Selmar groups; elliptic curves; plus/minus Iwasawa main conjectureReferences:
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