This is an announcement for the paper "Banach spaces with polynomial numerical index 1" by Han Ju Lee. Abstract: We characterize Banach spaces with polynomial numerical index 1 when they have the Radon-Nikod\'ym property. The holomorphic numerical index is introduced and the characterization of the Banach space with holomorphic numerical index 1 is obtained when it has the Radon-Nikod\'ym property. Archive classification: math.FA Mathematics Subject Classification: 46G25; 46B20; 46B22 The source file(s), R070723.tex: 25404 bytes, is(are) stored in gzipped form as 0708.0055.gz with size 8kb. The corresponding postcript file has gzipped size 66kb. Submitted from: hahnju@postech.ac.kr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0708.0055 or http://arXiv.org/abs/0708.0055 or by email in unzipped form by transmitting an empty message with subject line uget 0708.0055 or in gzipped form by using subject line get 0708.0055 to: math@arXiv.org.