1996/10/23 by Harris, Michael, Tilouine, Jacques
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.math/9610228
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,ℤ). We suppose κ≥ 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≥ λ+ μ.