Journal Article Congruence Primes of the Kim-Ramakrishnan-Shahidi Lift

KATSURADA, Hidenori  ,  TAKEMORI, Sho

25 ( 3 )  , pp.332 - 346 , 2016 , Taylor & Francis
ISSN:1058-64581944-950x
NCID:AA10926641
Description
For a primitive form f of weight k for SL2(Z), let KS(f) be the Kim-Ramakrishnan-Shahidi (K-R-S) lift of f to the space of cusp forms of weight det(k+1)circle times Sym(k-2) for Sp(2)(Z). Based on some working hypothesis, we propose a conjecture, which relates the ratio KS(f), KS(f)/< f, f >(3) of the periods (Petersson norms) to the symmetric 6th L-value L(3k - 2, f, Sym(6)) of f. From this, we also propose that a prime ideal dividing the (conjectural) algebraic part L(3k - 2, f, Sym(6)) of L(3k - 2, f, Sym(6)) gives a congruence between the K-R-S lift and non-K-R-S lift, and test this conjecture numerically.
Full-Text

https://muroran-it.repo.nii.ac.jp/?action=repository_action_common_download&item_id=8937&item_no=1&attribute_id=24&file_no=1

Number of accesses :  

Other information