Selberg eigenvalue conjecture

Target entity: Selberg eigenvalue conjecture
Context triple: [Ramanujan–Petersson conjecture, relatedProblem, Selberg eigenvalue conjecture]

• A. Selberg trace formula
  The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
• B. Ramanujan–Petersson conjecture
  The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
• C. Hilbert–Pólya conjecture
  The Hilbert–Pólya conjecture is an unproven idea in number theory suggesting that the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a suitable self-adjoint operator, offering a potential spectral approach to proving the Riemann hypothesis.
• D. Selberg class
  The Selberg class is a collection of Dirichlet series with specific analytic properties introduced to generalize and axiomatize L-functions in number theory.
• E. Selberg zeta function
  The Selberg zeta function is an analytic function associated with the lengths of closed geodesics on a Riemannian manifold, playing a central role in spectral theory and the study of automorphic forms.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Selberg eigenvalue conjecture
Target entity description: The Selberg eigenvalue conjecture is a major open problem in analytic number theory and spectral theory that predicts a specific lower bound for the nontrivial eigenvalues of the Laplace operator on certain arithmetic hyperbolic surfaces.

• A. Selberg trace formula
  The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
• B. Ramanujan–Petersson conjecture
  The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
• C. Hilbert–Pólya conjecture
  The Hilbert–Pólya conjecture is an unproven idea in number theory suggesting that the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a suitable self-adjoint operator, offering a potential spectral approach to proving the Riemann hypothesis.
• D. Selberg class
  The Selberg class is a collection of Dirichlet series with specific analytic properties introduced to generalize and axiomatize L-functions in number theory.
• E. Selberg zeta function
  The Selberg zeta function is an analytic function associated with the lengths of closed geodesics on a Riemannian manifold, playing a central role in spectral theory and the study of automorphic forms.
• F. None of above. chosen