Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: generalized Ramanujan–Petersson conjecture for GL(n) | Statement: [Ramanujan–Petersson conjecture, inspired, generalized Ramanujan–Petersson conjecture for GL(n)]

Target entity: generalized Ramanujan–Petersson conjecture for GL(n)
Context triple: [Ramanujan–Petersson conjecture, inspired, generalized Ramanujan–Petersson conjecture for GL(n)]

• A. Ramanujan–Petersson conjecture chosen
  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.
• B. Euler products for automorphic L-functions
  Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
• C. Siegel’s theorem on zeros of L-functions
  Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
• D. Deligne bound for Fourier coefficients of modular forms
  The Deligne bound for Fourier coefficients of modular forms is a deep result in number theory, proved by Pierre Deligne, that gives optimal size estimates for the Fourier coefficients of cusp forms and confirms the Ramanujan–Petersson conjecture for modular forms.
• E. Serre’s conjecture on Galois representations
  Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.