Congruence Primes of the Kim-Ramakrishnan-Shahidi Lift

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Abstract

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.

Journal

  • Experimental Mathematics

    Experimental Mathematics 25(3), 332-346, 2016

    Taylor & Francis

Codes

  • NII Article ID (NAID)
    120005767586
  • NII NACSIS-CAT ID (NCID)
    AA10926641
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    1058-6458
  • Data Source
    IR 
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