Lower bounds for moments of L -functions

DOI10.1073/pnas.0501723102zbMath1159.11317arXivmath/0502042OpenAlexW2057903655WikidataQ33784485 ScholiaQ33784485MaRDI QIDQ5385864

Ze'ev Rudnick, Kannan Soundararajan

Publication date: 7 May 2008

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0502042

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Related Items (42)

Quantum variance for dihedral Maass forms ⋮ Higher integral moments of automorphic \(L\)-functions in short intervals ⋮ NEGATIVE VALUES OF THE RIEMANN ZETA FUNCTION ON THE CRITICAL LINE ⋮ Simple zeros of modular L -functions ⋮ Lower bounds of discrete moments of the derivatives of the Riemann zeta-function on the critical line ⋮ The sixth power moment of Dirichlet \(L\)-functions ⋮ Moments of moments of primes in arithmetic progressions ⋮ Lower bounds for negative moments of ζ′(ρ)$\zeta ^{\prime }(\rho )$ ⋮ Lower bounds for higher moments of the twisted \(L\)-functions ⋮ Breaking the \(\frac{1}{2}\)-barrier for the twisted second moment of Dirichlet \(L\)-functions ⋮ Lower bounds for the moments of the derivatives of the Riemann zeta-function and Dirichlet \(L\)-functions ⋮ Selberg's central limit theorem for quadratic Dirichlet \(L\)-functions over function fields ⋮ Moments and distribution of central \(L\)-values of quadratic twists of elliptic curves ⋮ The second and fourth moments of theta functions at their central point ⋮ Rudnick and Soundararajan's theorem for function fields ⋮ Upper bounds for discrete moments of the derivatives of the Riemann zeta-function on the critical line ⋮ EXPONENTIAL MOMENTS OF THE ARGUMENT OF THE RIEMANN ZETA FUNCTION ON THE CRITICAL LINE ⋮ The distribution of values of zeta and \(L\)-functions ⋮ A Discrete Mean Value of the Derivative of the Riemann Zeta Function ⋮ Moments of quadratic twists of elliptic curve \(L\)-functions over function fields ⋮ SHIFTED MOMENTS OF ‐FUNCTIONS AND MOMENTS OF THETA FUNCTIONS ⋮ Continuous lower bounds for the moments of Dedekind zeta-functions ⋮ A note on a conjecture of Gonek ⋮ Lower bound for the higher moment of symmetric square \(L\)-functions ⋮ The eighth moment of Dirichlet \(L\)-functions ⋮ On a conjecture of Montgomery and Soundararajan ⋮ Extreme values of zeta and \(L\)-functions ⋮ CONTINUOUS LOWER BOUNDS FOR MOMENTS OF ZETA ANDL‐FUNCTIONS ⋮ Upper bounds for the moments of derivatives of Dirichlet \(L\)-functions ⋮ Lower bound for higher moments of the mixed product of twisted \(L\)-functions ⋮ On fractional power moments of \(L\)-functions associated with certain cusp forms ⋮ THE FOURTH MOMENT OF DIRICHLET L-FUNCTIONS FOR THE RATIONAL FUNCTION FIELD ⋮ Moments of the Riemann zeta function ⋮ The sixth moment of automorphic \(L\)-functions ⋮ A spectral reciprocity formula and non-vanishing for \(L\)-functions on \(\mathrm{GL}(4)\times\mathrm{GL}(2)\) ⋮ The second moment of quadratic Dirichlet \(L\)-functions ⋮ Lower bounds for discrete negative moments of the Riemann zeta function ⋮ Bounds for moments of cubic and quartic Dirichlet \(L\)-functions ⋮ Moments of \(L\)-functions attached to the twist of modular form by Dirichlet characters ⋮ Moments of quadratic Dirichlet \(L\)-functions over function fields ⋮ The second moment of twisted modular \(L\)-functions ⋮ The Second Moment Theory of Families of 𝐿-Functions–The Case of Twisted Hecke 𝐿-Functions

Cites Work

• Random matrix theory and \(L\)-functions at \(s=1/2\).
• Random matrix theory and \(\zeta(1/2+it)\).

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