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$p$-ADIC EISENSTEIN SERIES AND 
$L$-FUNCTIONS OF CERTAIN CUSP FORMS ON DEFINITE UNITARY GROUPS
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 15 / Issue 3 / July 2016
- Published online by Cambridge University Press:
- 21 November 2014, pp. 471-510
- Print publication:
- July 2016
-
- Article
- Export citation
-
We construct
$p$-adic families of Klingen–Eisenstein series and 
$L$-functions for cusp forms (not necessarily ordinary) unramified at an odd prime 
$p$ on definite unitary groups of signature 
$(r,0)$ (for any positive integer 
$r$) for a quadratic imaginary field 
${\mathcal{K}}$ split at 
$p$. When 
$r=2$, we show that the constant term of the Klingen–Eisenstein family is divisible by a certain 
$p$-adic 
$L$-function.
