Finding meaning in error terms

DOI10.1090/S0273-0979-08-01207-XzbMath1229.11001OpenAlexW2057308671MaRDI QIDQ3498863

Barry Mazur

Publication date: 19 May 2008

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

Full work available at URL: https://doi.org/10.1090/s0273-0979-08-01207-x

zbMATH Keywords

surveyGalois representationserror termspotential automorphySato-Tate conjecture for elliptic curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Modular and automorphic functions (11F03) Galois representations (11F80) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items

The Sato–Tate Distribution and the Values of Fourier Coefficients of Modular Newforms, Joint value-distribution of \(L\)-functions and discrepancy of Hecke eigenvalues, Equidistribution of signs for modular eigenforms of half integral weight, On the ranks of elliptic curves with isogenies, Some aspects and applications of the Riemann hypothesis over finite fields, The explicit Sato-Tate Conjecture and densities pertaining to Lehmer-type questions, The work of Barry Mazur, Effective forms of the Sato-Tate conjecture, Is it plausible?, Arithmetic applications of the Langlands program, On modular signs, Special values of motivic \(L\)-functions and zeta-polynomials for symmetric powers of elliptic curves, Moments of the error term in the Sato-Tate law for elliptic curves, Galois representations, automorphic forms, and the Sato-Tate conjecture, Chebyshev’s bias for analyticL-functions, DEFORMATIONS OF GALOIS REPRESENTATIONS AND THE THEOREMS OF SATO–TATE AND LANG–TROTTER, Knots which behave like the prime numbers, On the Rank and the Convergence Rate Toward the Sato–Tate Measure, Book Review: Convolution and equidistribution: Sato-Tate theorems for finite fields Mellin transforms

Uses Software

• SageMath
• ecdata

Cites Work

• Serre's modularity conjecture: the level one case
• Moduli of finite flat group schemes, and modularity
• A family of Calabi-Yau varieties and potential automorphy
• Automorphy for some \(l\)-adic lifts of automorphic mod \(l\) Galois representations. With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.
• Modularity of 2-adic Barsotti-Tate representations
• The existence of infinitely many supersingular primes for every elliptic curve over \(\mathbb Q\).
• On the Ramanujan conjecture and finiteness of poles for certain \(L\)-functions
• La conjecture de Weil. II
• Frobenius distributions in \(\mathrm{GL}_2\)-extensions. Distribution of Frobenius automorphisms in \(\mathrm{GL}_2\)-extensions of the rational numbers
• On the functional equations satisfied by Eisenstein series
• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• La conjecture de Weil. I
• Cuspidality of symmetric powers with applications.
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• A remark on the Sato-Tate conjecture
• Rankin-Selberg Convolutions
• On Certain L-Functions
• Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Calculation of values of 𝐿-functions associated to elliptic curves
• Twists of a General Class of L-Functions by Highly Ramified Characters
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Tauberian Theory
• Chebyshev's Bias
• Prime Number Races
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