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The Weil bound for generalized Kloosterman sums of half-integral weight

  • Nickolas Andersen EMAIL logo , Gradin Anderson and Amy Woodall
Published/Copyright: June 26, 2024
Forum Mathematicum
From the journal Forum Mathematicum Volume 37 Issue 3

Abstract

Let L be an even lattice of odd rank with discriminant group L ′ / L , and let α , β ∈ L ′ / L . We prove the Weil bound for the Kloosterman sums S α , β ⁢ ( m , n , c ) of half-integral weight for the Weil Representation attached to L. We obtain this bound by proving an identity that relates a divisor sum of Kloosterman sums to a sparse exponential sum. This identity generalizes Kohnen’s identity for plus space Kloosterman sums with the theta multiplier system.

Keywords: Kloosterman sums; Weil representation; Weil bound
MSC 2020: 11L05; 11L07

Communicated by Jan Bruinier

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Received: 2023-10-17
Revised: 2024-05-01
Published Online: 2024-06-26
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Square-integrable representations and the coadjoint action of solvable Lie groups
  3. Deviation probabilities for extremal eigenvalues of large Chiral non-Hermitian random matrices
  4. Nef vector bundles on a hyperquadric with first Chern class two
  5. Scaling spectrum of a class of self-similar measures with product form on ℝ
  6. Idempotent decomposition of regularity and characterization for the accumulation of associated spectrum
  7. Geodesic orbit Randers metrics in homogeneous bundles over generalized Stiefel manifolds
  8. Proof of some conjectures of Guo and of Tang
  9. On Absolute and Quantitative Subspace Theorems
  10. Birational equivalence of the Zassenhaus varieties for basic classical Lie superalgebras and their purely-even reductive Lie subalgebras in odd characteristic
  11. Geometric approach to the Moore–Penrose inverse and the polar decomposition of perturbations by operator ideals
  12. The Weil bound for generalized Kloosterman sums of half-integral weight
  13. Relative Rota–Baxter groups and skew left braces
  14. Asai gamma factors over finite fields
  15. Representations of non-finitely graded Lie algebras related to Virasoro algebra
  16. Multiple solutions for fractional elliptic systems
  17. Arithmetic Bohr radius for the Minkowski space
  18. On Strichartz estimates for many-body Schrödinger equation in the periodic setting
https://doi.org/10.1515/forum-2023-0367
Keywords for this article
Kloosterman sums; Weil representation; Weil bound

Articles in the same Issue

  1. Frontmatter
  2. Square-integrable representations and the coadjoint action of solvable Lie groups
  3. Deviation probabilities for extremal eigenvalues of large Chiral non-Hermitian random matrices
  4. Nef vector bundles on a hyperquadric with first Chern class two
  5. Scaling spectrum of a class of self-similar measures with product form on ℝ
  6. Idempotent decomposition of regularity and characterization for the accumulation of associated spectrum
  7. Geodesic orbit Randers metrics in homogeneous bundles over generalized Stiefel manifolds
  8. Proof of some conjectures of Guo and of Tang
  9. On Absolute and Quantitative Subspace Theorems
  10. Birational equivalence of the Zassenhaus varieties for basic classical Lie superalgebras and their purely-even reductive Lie subalgebras in odd characteristic
  11. Geometric approach to the Moore–Penrose inverse and the polar decomposition of perturbations by operator ideals
  12. The Weil bound for generalized Kloosterman sums of half-integral weight
  13. Relative Rota–Baxter groups and skew left braces
  14. Asai gamma factors over finite fields
  15. Representations of non-finitely graded Lie algebras related to Virasoro algebra
  16. Multiple solutions for fractional elliptic systems
  17. Arithmetic Bohr radius for the Minkowski space
  18. On Strichartz estimates for many-body Schrödinger equation in the periodic setting
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