On extra zeros of \(p\)-adic Rankin-Selberg \(L\)-functions. (English) Zbl 1532.11153
St. Petersbg. Math. J. 34, No. 6, 929-989 (2023) and Algebra Anal. 34, No. 6, 55-134 (2022).
Summary: A version of the extra-zero conjecture, formulated by the first named author, is proved for \(p\)-adic \(L\)-functions associated with Rankin-Selberg convolutions of modular forms of the same weight. This result provides an evidence in support of this conjecture in the noncritical case, which remained essentially unstudied.
MSC:
| 11R23 | Iwasawa theory |
| 11F80 | Galois representations |
| 11F85 | \(p\)-adic theory, local fields |
| 11S25 | Galois cohomology |
| 11G40 | \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture |
| 14F30 | \(p\)-adic cohomology, crystalline cohomology |
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