Moments and distribution of central \(L\)-values of quadratic twists of elliptic curves

DOI10.1007/s00222-015-0582-zzbMath1396.11098arXiv1403.7067OpenAlexW2166029767MaRDI QIDQ896256

Maksym Radziwiłł, Kannan Soundararajan

Publication date: 9 December 2015

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.7067

zbMATH Keywords

elliptic curvesTate-Shafarevich groupquadratic twists

Mathematics Subject Classification ID

(L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (33)

Dirichlet \(L\)-functions of quadratic characters of prime conductor at the central point ⋮ Bounds for moments of modular $L$-functions to a fixed modulus ⋮ Multiplicative functions in short intervals ⋮ Quantum variance for dihedral Maass forms ⋮ Moments of the products of quadratic twists of automorphic \(L\)-functions ⋮ Signs of Fourier coefficients of half-integral weight modular forms ⋮ Upper bounds for fractional joint moments of the Riemann zeta function ⋮ Simultaneous supersingular reductions of CM elliptic curves ⋮ On the distribution of coefficients of half-integral weight modular forms and the Bruinier–Kohnen conjecture ⋮ The Ratios Conjecture and upper bounds for negative moments of 𝐿-functions over function fields ⋮ Lower bounds for moments of zeta and L$L$‐functions revisited ⋮ Moments of moments of primes in arithmetic progressions ⋮ Breaking the \(\frac{1}{2}\)-barrier for the twisted second moment of Dirichlet \(L\)-functions ⋮ Limit laws for rational continued fractions and value distribution of quantum modular forms ⋮ Selberg's central limit theorem for quadratic Dirichlet \(L\)-functions over function fields ⋮ ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL CUSP FORMS OF DEGREE 2 ⋮ Extreme central \(L\)-values of almost prime quadratic twists of elliptic curves ⋮ Mollified moments of cubic Dirichlet \(L\)-functions over the Eisenstein field ⋮ Negative moments of the Riemann zeta-function ⋮ On the splitting conjecture in the hybrid model for the Riemann zeta function ⋮ The distribution of values of zeta and \(L\)-functions ⋮ Moments of quadratic twists of elliptic curve \(L\)-functions over function fields ⋮ Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves ⋮ On the typical size and cancellations among the coefficients of some modular forms ⋮ On a conjecture of Montgomery and Soundararajan ⋮ Quantum unique ergodicity for half-integral weight automorphic forms ⋮ Integral moments of automorphic L-functions ⋮ Bounds for moments of cubic and quartic Dirichlet \(L\)-functions ⋮ Moments of quadratic Dirichlet \(L\)-functions over function fields ⋮ Nonvanishing for cubic L-functions ⋮ Behaviour of the Order of Tate–Shafarevich Groups for the Quadratic Twists of $$X_0(49)$$ ⋮ The Second Moment Theory of Families of 𝐿-Functions–The Case of Twisted Hecke 𝐿-Functions ⋮ The first moment of quadratic twists of modular $L$-functions

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