Modular functions and the uniform distribution of CM points

DOI10.1007/s00208-005-0706-7zbMath1091.11012OpenAlexW2009017436MaRDI QIDQ818547

William Duke

Publication date: 21 March 2006

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-005-0706-7

zbMATH Keywords

Poincaré seriesKloosterman sumstraces of singular moduli

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Modular and automorphic functions (11F03)

Related Items

Hilbert class polynomials and traces of singular moduli ⋮ Bases of spaces of harmonic weak Maass forms and Shintani lifts of harmonic weak Maass forms ⋮ Niebur-Poincaré series and traces of singular moduli ⋮ Arithmetic properties of coefficients of half-integral weight Maass-Poincaré series ⋮ Nonvanishing of Hecke \(L\)-functions and the Bloch-Kato conjecture ⋮ Some remarks on Hurwitz-Kronecker class numbers and traces of singular moduli ⋮ The asymptotic distribution of Andrews' smallest parts function ⋮ Weierstrass mock modular forms and elliptic curves ⋮ Effective estimates for traces of singular moduli ⋮ The asymptotic distribution of traces of Maass-Poincaré series ⋮ Unnamed Item ⋮ Singular moduli and the distribution of partition ranks modulo 2 ⋮ Modularity of Galois traces of class invariants ⋮ Modular invariants for real quadratic fields and Kloosterman sums ⋮ Cycle integrals of the \(j\)-function on Markov geodesics ⋮ Cycle integrals of the \(j\)-function and mock modular forms ⋮ The asymptotic distribution of traces of cycle integrals of the \(j\)-function ⋮ Singular invariants and coefficients of harmonic weak Maass forms of weight \(5/2\) ⋮ Exact formulas for traces of singular moduli of higher level modular functions ⋮ Ramanujan’s mock theta functions ⋮ Regularized theta lifts and Niebur-type Poincaré series on \(n\)-dimensional hyperbolic space ⋮ Kloosterman sums and traces of singular moduli ⋮ Equidistribution of Heegner points and the partition function ⋮ ARITHMETIC PROPERTIES OF TRACES OF SINGULAR MODULI ON CONGRUENCE SUBGROUPS ⋮ Zagier-lift type arithmetic in harmonic weak Maass forms ⋮ Effective bounds for traces of singular moduli ⋮ Values of harmonic weak Maass forms on Hecke orbits ⋮ Heegner points and Eisenstein series

Cites Work

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