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Generalized Ramanujan conjecture over general imaginary quadratic fields

  • Maki Nakasuji EMAIL logo
Veröffentlicht/Copyright: 19. Januar 2012
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 24 Heft 1

Abstract.

The new bound toward the generalized Ramanujan conjecture for GLn(𝐀𝐐) is given by Kim–Sarnak [4]. We generalize it to that for GLn(𝐀F) with F being an imaginary quadratic field. Applying the obtained bound to the automorphic representation of GL5 gives the following estimate for the first positive eigenvalue of the Laplacian on L2(3), where is any congruence subgroups of SL2(F) with F the ring of integers of F: 1()0.952.

Keywords.: Generalized Ramanujan conjecture; Ramanujan–Selberg conjecture; imaginary quadratic fields; symmetric square -function
Received: 2009-03-10
Revised: 2010-02-24
Published Online: 2012-01-19
Published in Print: 2012-January

© 2012 by Walter de Gruyter Berlin Boston

Artikel in diesem Heft

  1. Prelims
  2. The Lerch zeta function I. Zeta integrals
  3. The Lerch zeta function II. Analytic continuation
  4. Generalized Ramanujan conjecture over general imaginary quadratic fields
  5. Almost prime values of the order of elliptic curves over finite fields
  6. Manifolds associated with (2)n+1-colored regular graphs
  7. A Steinness criterion for Stein fibrations
  8. Crown-free highly arc-transitive digraphs
  9. Pitt's inequality and the fractional Laplacian: Sharp error estimates
  10. On affine group actions on Stein manifolds
https://doi.org/10.1515/form.2011.050
Schlagwörter fĂŒr diesen Artikel
Generalized Ramanujan conjecture; Ramanujan–Selberg conjecture; imaginary quadratic fields; symmetric square -function

Artikel in diesem Heft

  1. Prelims
  2. The Lerch zeta function I. Zeta integrals
  3. The Lerch zeta function II. Analytic continuation
  4. Generalized Ramanujan conjecture over general imaginary quadratic fields
  5. Almost prime values of the order of elliptic curves over finite fields
  6. Manifolds associated with (2)n+1-colored regular graphs
  7. A Steinness criterion for Stein fibrations
  8. Crown-free highly arc-transitive digraphs
  9. Pitt's inequality and the fractional Laplacian: Sharp error estimates
  10. On affine group actions on Stein manifolds
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