Matches in SemOpenAlex for { <https://semopenalex.org/work/W2138676592> ?p ?o ?g. }
- W2138676592 abstract "Let $pi$ be a cuspidal automorphic representation of $operatorname{GL}$ over a totally real number field $F$. Assume that $pi$ is non-dihedral, hence not induced from a Hecke character of a quadratic extension of $F$. Let $K$ be a totally imaginary quadratic extension of $F$. We estimate central values of the $operatorname{GL}_2 times operatorname{GL}_2$ Rankin-Selberg $L$-functions associated to $pi$ times representations induced from Hecke characters of $K$ which are ramified only at a given prime ideal $mathfrak{p}$ of $F$. More specifically, we use spectral decompositions of shifted convolution sums and relations to Fourier-Whittaker coefficients of metaplectic forms to obtain nonvanishing estimates (averaging over ring class characters of a given exact order). When $pi$ corresponds to a holomorphic Hilbert modular form of arithmetic weight $k geq 2$, we then derive finer results from the rationality theorems of Shimura, together with the existence of suitable $mathfrak{p}$-adic $L$-functions. This allows us to generalize the theorems of Rohrlich, Vatsal, and Cornut-Vatsal to this setting. Finally, in a self-contained appendix, we explain how to use these results to deduce bounds for Mordell-Weil ranks of the associated $operatorname{GL}_2$-type abelian varieties via existing Iwasawa main conjecture divisibilities." @default.
- W2138676592 created "2016-06-24" @default.
- W2138676592 creator A5007634405 @default.
- W2138676592 date "2012-07-06" @default.
- W2138676592 modified "2023-09-27" @default.
- W2138676592 title "Rankin-Selberg L-functions in cyclotomic towers, III" @default.
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