http://swrc.ontoware.org/ontology#Article
Congruence Primes of the Kim-Ramakrishnan-Shahidi Lift
en
Kim-Ramakrishnan-Shahidi lif
symmetric 6-th L function
congruence
KATSURADA Hidenori
TAKEMORI Sho
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.
Experimental Mathematics
25
3
332-346
2016
Taylor & Francis
info:doi/10.1080/10586458.2015.1070777
410
1058-6458
1944-950X
AA10926641
This is an Accepted Manuscript of an article published by Taylor & Francis in Experimental Mathematics on 02/07/2016, available online: http://wwww.tandfonline.com/10.1080/10586458.2015.1070777
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