I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2010, VOLUME 16, NUMBER 5, PAGES 139-160
On zeta functions and families of Siegel modular forms
A. A. Panchishkin
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a prime, and let
be the Siegel modular
group of genus .
The paper is concerned with -adic families of zeta
functions and -functions of Siegel
modular forms, the latter are described in terms of motivic
attached to ; their
analytic properties are given.
Critical values for the spinor -functions are discussed
in relation to -adic constructions.
Rankin's lemma of higher genus is established.
A general conjecture on a lifting of modular forms from
Constructions of -adic families of Siegel
modular forms are given using Ikeda--Miyawaki constructions.
Last modified: May 30, 2011