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A Shimura–Shintani correspondence for rigid analytic cocycles of higher weight

  • Isabella Negrini ORCID logo EMAIL logo
Published/Copyright: February 28, 2023
Forum Mathematicum
From the journal Forum Mathematicum Volume 35 Issue 2

Abstract

This paper takes the first steps towards a systematic study of additive rigid meromorphic cocycles of higher weight. These were introduced by Darmon and Vonk, who focused on additive cocycles of weight two and their multiplicative lifts. After classifying certain rigid meromorphic cocycles of weight 2 ⁢ k , we construct an explicit holomorphic kernel function realizing a Shimura–Shintani style correspondence from modular forms of weight k + 1 / 2 and level 4 ⁢ p 2 to rigid analytic cocycles of weight 2 ⁢ k on SL 2 ⁡ ( ℤ ⁢ [ 1 / p ] ) .

Keywords: Algebraic number theory; Shimura–Shintani correspondence, theta correspondence; rigid meromorphic cocycles
MSC 2010: 11S99

Communicated by Jan Bruinier

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Received: 2022-08-11
Revised: 2022-12-11
Published Online: 2023-02-28
Published in Print: 2023-03-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. On the asymptotics of the shifted sums of Hecke eigenvalue squares
  3. On the splitting conjecture in the hybrid model for the Riemann zeta function
  4. Almost Dedekind domains without radical factorization
  5. Groups in which the centralizer of any non-central primary element is maximal
  6. GKM actions on cohomogeneity one manifolds
  7. Gruenberg–Kegel graphs: Cut groups, rational groups and the prime graph question
  8. Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds
  9. Higher differentiability for bounded solutions to a class of obstacle problems with (p,q)-growth
  10. Measures of noncompactness of interpolated polynomials
  11. The homotopy category of acyclic complexes of pure-projective modules
  12. The Gelfand–Kirillov dimension of Hecke–Kiselman algebras
  13. Sharp Li–Yau inequalities for Dunkl harmonic oscillators
  14. A Shimura–Shintani correspondence for rigid analytic cocycles of higher weight
  15. Free polynilpotent groups and the Magnus property
https://doi.org/10.1515/forum-2022-0235
Keywords for this article
Algebraic number theory; Shimura–Shintani correspondence, theta correspondence; rigid meromorphic cocycles

Articles in the same Issue

  1. Frontmatter
  2. On the asymptotics of the shifted sums of Hecke eigenvalue squares
  3. On the splitting conjecture in the hybrid model for the Riemann zeta function
  4. Almost Dedekind domains without radical factorization
  5. Groups in which the centralizer of any non-central primary element is maximal
  6. GKM actions on cohomogeneity one manifolds
  7. Gruenberg–Kegel graphs: Cut groups, rational groups and the prime graph question
  8. Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds
  9. Higher differentiability for bounded solutions to a class of obstacle problems with (p,q)-growth
  10. Measures of noncompactness of interpolated polynomials
  11. The homotopy category of acyclic complexes of pure-projective modules
  12. The Gelfand–Kirillov dimension of Hecke–Kiselman algebras
  13. Sharp Li–Yau inequalities for Dunkl harmonic oscillators
  14. A Shimura–Shintani correspondence for rigid analytic cocycles of higher weight
  15. Free polynilpotent groups and the Magnus property
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