p-adic measures and square roots of triple product L-functions
| dc.creator | Harris, Michael | |
| dc.creator | Tilouine, Jacques | |
| dc.date | 1996-10-23 | |
| dc.date.accessioned | 2026-07-07T09:15:39Z | |
| dc.date.available | 2026-07-07T09:15:39Z | |
| dc.description | Let p be a prime number, and let f, g, and h be three modular forms of weights $κ$, $λ$, and $μ$ for $SL(2,\Bbb{Z})$. We suppose $κ\geq λ+ μ$. In joint work with Kudla, one of the authors obtained a formula for the normalized {\it square root} of the value at $s = {1/2}(κ+ λ+ μ- 2)$ (the {\it central critical value}) of the triple product $L(s,f,g,h)$. We apply this formula, letting $f$ (and thus $κ$) vary in a $p$-adic analytic family ${\bold f}$ of ordinary modular forms (a Hida family). By modifying Hida's construction of the $p$-adic Rankin-Selberg convolution, we obtain a generalized $p$-adic measure whose associated analytic function gives a $p$-adic interpolation of the square roots of the central critical values of $L(s,f,g,h)$, normalized by certain universal correction factors. The archimedean correction factor is not determined explicitly. This is an example of what appears to be a very general phenomenon of $p$-adic interpolation of normalized square roots of $L$-functions along the so-called "anti-cyclotomic hyperplane." We note that the $p$-adic triple product itself has not been constructed in the half-space $κ\geq λ+ μ$. | |
| dc.identifier | https://arxiv.org/abs/math/9610228 | |
| dc.identifier | http://arxiv.org/abs/math/9610228 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153087 | |
| dc.subject | Number Theory | |
| dc.title | p-adic measures and square roots of triple product L-functions | |
| dc.type | text |