Geometric invariants for real quadratic fields

DOI10.4007/annals.2016.184.3.8zbMath1372.11056OpenAlexW2520783889MaRDI QIDQ338429

Özlem Imamoḡlu, William Duke, Árpad Tóth

Publication date: 4 November 2016

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: http://real.mtak.hu/62299/1/Geometric-Invariants--resubmit.pdf

zbMATH Keywords

equidistributionmodular formsreal quadratic fieldsclosed geodesicssubconvexity

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Holomorphic modular forms of integral weight (11F11) Class numbers, class groups, discriminants (11R29)

Related Items (15)

A symplectic restriction problem ⋮ The variance of closed geodesics in balls and annuli on the modular surface ⋮ Equidistribution in shrinking sets and \(L^4\)-norm bounds for automorphic forms ⋮ Shintani correspondence for Maass forms of level \(N\) and prehomogeneous zeta functions ⋮ The Katok-Sarnak formula for higher weights ⋮ Effective estimates for traces of singular moduli ⋮ Error approximation for backwards and simple continued fractions ⋮ Modular invariants for real quadratic fields and Kloosterman sums ⋮ Bounds for twisted symmetric square L-functions via half-integral weight periods ⋮ Genus character L‐functions of quadratic orders and class numbers ⋮ Hybrid subconvexity for class group \(L \)-functions and uniform sup norm bounds of Eisenstein series ⋮ Quantum unique ergodicity for half-integral weight automorphic forms ⋮ Kronecker's first limit formula, revisited ⋮ Hybrid subconvexity and the partition function ⋮ Eisenstein series of even weight 𝑘≥2 and integral binary quadratic forms

Cites Work

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• Cycle integrals of the \(j\)-function and mock modular forms
• Die Funktionalgleichungen einiger Dirichletscher Reihen
• Über die räumliche Verteilung der Punkte in Gittern mit indefiniter Metrik. (On the spatial distribution of the points in lattices with indefinite metric)
• Fourier coefficients and modular forms of half-integral weight
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• On Petersson products of not necessarily cuspidal modular forms
• Eisenstein series of \(1\over 2\)-integral weight and the mean value of real Dirichlet L-series
• 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
• Bounds for automorphic \(L\)-functions
• Heegner points, cycles and Maass forms
• The cubic moment of central values of automorphic \(L\)-functions
• Coding of closed geodesics after Gauss and Morse
• Sums of Kloosterman sums
• A Kronecker limit formula for real quadratic fields
• Hilbert modular surfaces
• The distribution of closed geodesics on the modular surface, and Duke's Theorem
• Kloosterman sums and traces of singular moduli
• Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I, II. (The eigenvalue problem of automorphic forms in the hyperbolic plane. I. II)
• On Poincaré's theorem for fundamental polygons
• L-Series, modular imbeddings, and signatures
• On modular forms of half integral weight
• Weyl-type hybrid subconvexity bounds for twisted \(L\)-functions and Heegner points on shrinking sets
• Weyl Sums for Quadratic Roots
• Computation of Maass waveforms with nontrivial multiplier systems
• On Character Sums and L-Series^†
• Effective computation of Maass cusp forms
• Hybrid bounds for twisted L-functions
• A generalized Kohnen-Zagier formula for Maass forms
• On construction of holomorphic cusp forms of half integral weight
• Fourier coefficients of the resolvent for a Fuchsian group.
• Cycle integrals of Maass forms of weight 0 and Fourier coefficients of Maass forms of weight 1/2
• A class of nonanalytic automorphic functions
• On the evaluation of Salié sums
• The Modular Groups of Hilbert and Siegel
• Grenzkreisgruppen und kettenbruchartige Algorithmen
• Class numbers of indefinite binary quadratic forms

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