Ordinary families of Klingen Eisenstein series on symplectic groups

Abstract

We construct ( n + 1 ) (n+1) -variable Hida families of Klingen Eisenstein series on Sp ⁡ ( 2 n + 2 ) \operatorname {Sp}(2n+2) for n n -variable Hida families on Sp ⁡ ( 2 n ) \operatorname {Sp}(2n) , and relate their images under the Siegel operator to p p -adic L L -functions. We also carry out some preliminary calculations of the non-degenerate Fourier coefficients of the constructed Klingen Eisenstein families.