Congruence Primes of the Kim-Ramakrishnan-Shahidi Lift

• 桂田, 英典

• 竹森, 翔

抄録

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.

収録刊行物

• Experimental Mathematics

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

  Taylor & Francis

キーワード

• Kim-Ramakrishnan-Shahidi lif
• symmetric 6-th L function
• congruence

詳細情報

• CRID: 1050282676657382400
• NII論文ID: 120005767586
• NII書誌ID: AA10926641
• ISSN: 1944950X
• ISSN: 10586458
• HANDLE: 10258/00008922
• Web Site: https://muroran-it.repo.nii.ac.jp/records/8937
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
  • IRDB
  • CiNii Articles