A generalized cubic moment and the Petersson formula for newforms
From MaRDI portal
Publication:1741821
DOI10.1007/s00208-018-1745-1zbMath1446.11069arXiv1608.06854OpenAlexW2517446171MaRDI QIDQ1741821
Matthew P. Young, Ian N. Petrow
Publication date: 7 May 2019
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1608.06854
Forms of half-integer weight; nonholomorphic modular forms (11F37) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11) Zeta and (L)-functions: analytic theory (11M99)
Related Items
Some recents advances on Duke’s equidistribution theorems ⋮ Subconvexity bounds for twisted 𝐿-functions, II ⋮ Analytic isolation of newforms of given level ⋮ The fifth moment of modular \(L\)-functions ⋮ A short note on sign changes and non-vanishing of Fourier coefficients of half-integral weight cusp forms ⋮ Concentration of closed geodesics in the homology of modular curves ⋮ Weyl-type bounds for twisted \(\mathrm{GL}(2)\) short character sums ⋮ Intersecting geodesics on the modular surface ⋮ Jacobi forms, Saito-Kurokawa lifts, their pullbacks and sup-norms on average ⋮ The fourth moment of Dirichlet \(L\)-functions along a coset and the Weyl bound ⋮ Oscillatory integrals with uniformity in parameters ⋮ Modular invariants for real quadratic fields and Kloosterman sums ⋮ The Weyl bound for Dirichlet \(L\)-functions of cube-free conductor ⋮ Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field ⋮ On the Ramanujan-Petersson conjecture for modular forms of half-integral weight ⋮ Level aspect of simultaneous nonvanishing for the central 𝐿-values associated to cusp forms ⋮ Burgess-like subconvexity for ⋮ On the Waldspurger formula and the metaplectic Ramanujan conjecture over number fields ⋮ Hybrid subconvexity and the partition function ⋮ The cubic moment of automorphic \(L\)-functions in the weight aspect ⋮ The asymptotic formula for the averages of the product of twisted \(L\)-functions
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Rankin-Selberg \(L\)-functions and the reduction of CM elliptic curves
- A twisted Motohashi formula and Weyl-subconvexity for \(L\)-functions of weight two cusp forms
- Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids
- The asymptotic distribution of traces of Maass-Poincaré series
- One-level density for holomorphic cusp forms of arbitrary level
- Fourier coefficients and 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
- Twists of newforms and pseudo-eigenvalues of \(W\)-operators
- Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
- Newforms and functional equations
- The cubic moment of central values of automorphic \(L\)-functions
- Mollification of the fourth moment of automorphic \(L\)-functions and arithmetic applications.
- Explicit calculations with Eisenstein series
- On ternary quadratic forms
- Comparison of Arakelov and Poincaré metrics on \(X_0(N)\)
- Distribution of Maass of holomorphic cusp forms
- Kloosterman sums in residue classes
- Oscillatory integrals with uniformity in parameters
- Central value of automorphic \(L\)-functions
- Hecke operators on \(\Gamma_0(m)\)
- A large sieve density estimate near \(\sigma = 1\)
- Modular functions of one variable. II. Proceedings international summer school, University of Antwerp, RUCA. July 17-August 3, 1972
- Analytic isolation of newforms of given level
- Weyl-type hybrid subconvexity bounds for twisted \(L\)-functions and Heegner points on shrinking sets
- The fifth moment of modular \(L\)-functions
- On the change of root numbers under twisting and applications
- Subconvexity and equidistribution of Heegner points in the level aspect
- Fourier coefficients of harmonic weak Maass forms and the partition function
- Formules de trace et non-annulation de fonctions L automorphes au niveau pν
- A Burgess-like subconvex bound for twisted L-functions
- Small eigenvalues of Laplacian for $Γ_{0}(N)$
- Hybrid bounds for twisted L-functions
- The first sign change of Fourier coefficients of cusp forms
- Uniform bounds for Fourier coefficients of theta-series with arithmetic applications
- REPRESENTATIONS OF INTEGERS BY TERNARY QUADRATIC FORMS
- Integral moments of L-functions
- Low lying zeros of families of \(L\)-functions
