Weyl-type hybrid subconvexity bounds for twisted \(L\)-functions and Heegner points on shrinking sets

DOI10.4171/JEMS/699zbMath1430.11067arXiv1405.5457MaRDI QIDQ2628340

Matthew P. Young

Publication date: 1 June 2017

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.5457

zbMATH Keywords

\(L\)-functionsequidistributionHeegner pointssubconvexity

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67)

Related Items (35)

Some recents advances on Duke’s equidistribution theorems ⋮ Hybrid subconvexity bounds for twisted \(L\)-functions on \(\mathrm{GL}(3)\) ⋮ The variance of closed geodesics in balls and annuli on the modular surface ⋮ Moments of central 𝐿-values for Maass forms over imaginary quadratic fields ⋮ Geometric invariants for real quadratic fields ⋮ Equidistribution in shrinking sets and \(L^4\)-norm bounds for automorphic forms ⋮ Prime geodesics and averages of the Zagier L-series ⋮ Double first moment for \(L(\frac{1}{2}, \operatorname{Sym}^2 f \times g)\) by applying Petersson's formula twice ⋮ On simultaneous nonvanishing of the central $L$-values ⋮ Weyl-type bounds for twisted \(\mathrm{GL}(2)\) short character sums ⋮ The asymptotic distribution of Andrews' smallest parts function ⋮ Wide moments of L-functions. I: Twists by class group characters of imaginary quadratic fields ⋮ Extreme values of L$L$‐functions of newforms ⋮ Unnamed Item ⋮ Jacobi forms, Saito-Kurokawa lifts, their pullbacks and sup-norms on average ⋮ Modular invariants for real quadratic fields and Kloosterman sums ⋮ The Weyl bound for Dirichlet \(L\)-functions of cube-free conductor ⋮ Bounds for a spectral exponential sum ⋮ A generalized cubic moment and the Petersson formula for newforms ⋮ A twisted Motohashi formula and Weyl-subconvexity for \(L\)-functions of weight two cusp forms ⋮ Hybrid subconvexity for class group \(L \)-functions and uniform sup norm bounds of Eisenstein series ⋮ Bounds for twists of \(\mathrm{GL}(3)\) \(L\)-functions ⋮ The Relative Trace Formula in Analytic Number Theory ⋮ The first moment of Maaß form symmetric square \(L\)-functions ⋮ Level aspect of simultaneous nonvanishing for the central 𝐿-values associated to cusp forms ⋮ Burgess-like subconvexity for ⋮ CM-points and lattice counting on arithmetic compact Riemann surfaces ⋮ On the random wave conjecture for dihedral Maaß forms ⋮ Maass forms and the mock theta function \(f(q)\) ⋮ Arithmetic exponent pairs for algebraic trace functions and applications ⋮ The additive problem for the number of representations as a sum of two squares ⋮ Hybrid subconvexity and the partition function ⋮ Subconvexity for twisted 𝐿-functions on 𝐺𝐿₃ over the Gaussian number field ⋮ The cubic moment of automorphic \(L\)-functions in the weight aspect ⋮ The asymptotic formula for the averages of the product of twisted \(L\)-functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bounds for the spectral mean value of central values of \(L\)-functions
• A twisted Motohashi formula and Weyl-subconvexity for \(L\)-functions of weight two cusp forms
• Bounds for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions and \(\mathrm{GL}(3)\) \(L\)-functions
• Gross-Zagier formula for \(\text{GL}_ 2\).
• The quantum unique ergodicity conjecture for thin sets
• Fourier coefficients of modular forms of half-integral weight
• Hyperbolic distribution problems and half-integral weight Maass forms
• Sur les coefficients de Fourier des formes modulaires de poids demi-entier
• Values of L-series of modular forms at the center of the critical strip
• Heegner points, cycles and Maass forms
• The cubic moment of central values of automorphic \(L\)-functions
• On sums of Hecke series in short intervals
• On the positivity of the central critical values of automorphic \(L\)-functions for \(GL(2)\)
• Distribution of Maass of holomorphic cusp forms
• Uniform bound for Hecke \(L\)-functions
• A large sieve density estimate near \(\sigma = 1\)
• The fifth moment of modular \(L\)-functions
• Subconvexity and equidistribution of Heegner points in the level aspect
• Subconvexity for twisted <i>L</i>-functions on GL(3)
• On Character Sums and L-Series^†
• Hybrid bounds for twisted L-functions
• Hybrid bounds for Dirichlet's L-function

This page was built for publication: Weyl-type hybrid subconvexity bounds for twisted \(L\)-functions and Heegner points on shrinking sets