The explicit Sato-Tate Conjecture and densities pertaining to Lehmer-type questions

DOI10.1090/tran/6793zbMath1429.11086arXiv1305.5283OpenAlexW3099487780WikidataQ123182889 ScholiaQ123182889MaRDI QIDQ2960439

Jesse Thorner, Jeremy Rouse

Publication date: 9 February 2017

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.5283

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Congruences for modular and (p)-adic modular forms (11F33) Fourier coefficients of automorphic forms (11F30)

Related Items

On the Chebotarev-Sato-Tate phenomenon ⋮ Pair correlation statistics for Sato-Tate sequences ⋮ Modular forms and an explicit Chebotarev variant of the Brun-Titchmarsh theorem ⋮ Elliptic curve variants of the least quadratic nonresidue problem and Linnik’s theorem ⋮ Higher moments of the pair correlation function for Sato-Tate sequences ⋮ The error term in the Sato-Tate conjecture ⋮ Metric number theory of Fourier coefficients of modular forms ⋮ Effective forms of the Sato-Tate conjecture ⋮ On conjectures of Sato-Tate and Bruinier-Kohnen ⋮ A short note on the Bruiner–Kohnen sign equidistribution conjecture and Halász’ theorem ⋮ Patterns of primes in the Sato-Tate conjecture ⋮ Extremal primes for elliptic curves without complex multiplication ⋮ The explicit Sato–Tate conjecture for primes in arithmetic progressions ⋮ Central limit theorems for elliptic curves and modular forms with smooth weight functions ⋮ Symmetric power functoriality for holomorphic modular forms

Uses Software

• Magma
• PARI/GP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A family of Calabi-Yau varieties and potential automorphy. II.
• Explicit formulae and the Lang-Trotter conjecture
• The existence of infinitely many supersingular primes for every elliptic curve over \(\mathbb Q\).
• Quelques applications du théorème de densité de Chebotarev
• Frobenius distributions in \(\mathrm{GL}_2\)-extensions. Distribution of Frobenius automorphisms in \(\mathrm{GL}_2\)-extensions of the rational numbers
• The Magma algebra system. I: The user language
• Ramanujan's ternary quadratic form
• Cuspidality of symmetric powers with applications.
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• On conjectures of Sato-Tate and Bruinier-Kohnen
• Atkin-Serre type conjectures for automorphic representations on \(\mathrm{GL}(2)\)
• Hecke operators on \(\Gamma_0(m)\)
• The vanishing of Ramanujan's function \(\tau(n)\)
• Critical zeros of Dirichlet L-functions
• Bounds for the Lang-Trotter Conjectures
• Ellitpic curves and modular functions
• Computational Aspects of Modular Forms and Galois Representations
• Perioden von Modulformen einer Variabler und Gruppencohomologie, I
• An application of the effective Sato-Tate conjecture
• Finding meaning in error terms
• Modular Forms and the Chebotarev Density Theorem
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x)
• The large sieve
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• On the Distribution of Supersingular Primes

This page was built for publication: The explicit Sato-Tate Conjecture and densities pertaining to Lehmer-type questions