The arithmetic of the values of modular functions and the divisors of modular forms
From MaRDI portal
Publication:4831288
DOI10.1112/S0010437X03000721zbMath1060.11019OpenAlexW2048381158MaRDI QIDQ4831288
Winfried Kohnen, Jan Hendrik Bruinier, Ken Ono
Publication date: 29 December 2004
Published in: Compositio Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1112/s0010437x03000721
Fourier expansionFourier coefficientsfundamental discriminantHurwitz class numberRamanujan's differential operator
Modular and automorphic functions (11F03) Congruences for modular and (p)-adic modular forms (11F33) Holomorphic modular forms of integral weight (11F11)
Related Items
POWERS OF THE ETA-FUNCTION AND HECKE OPERATORS ⋮ Hilbert class polynomials and traces of singular moduli ⋮ Explorations in the Theory of Partition Zeta Functions ⋮ Higher Weierstrass points on $X_{0}(p)$ ⋮ Stieltjes interlacing of the zeros of ⋮ Moonshine ⋮ Combinatorial properties of Rogers-Ramanujan type identities arising from Hall-Littlewood polynomials ⋮ ON THE VANISHING OF FOURIER COEFFICIENTS OF CERTAIN GENUS ZERO NEWFORMS ⋮ Orders at infinity of modular forms with Heegner divisors ⋮ On Generalized Modular forms and their Applications ⋮ Congruences concerning values of the modular functions \(j_n\) ⋮ A remark on congruences for coefficients of Faber polynomials ⋮ On values of weakly holomorphic modular functions at divisors of meromorphic modular forms ⋮ Asymptotic expansion of Fourier coefficients of reciprocals of Eisenstein series ⋮ On the generating function of a canonical basis for \(M_{0}^{!,\infty }(\Gamma)\) ⋮ Hecke equivariance of generalized Borcherds products of type \(O(2,1)\) ⋮ On product expansions of generalized modular forms ⋮ Hecke operators for weakly holomorphic modular forms and supersingular congruences ⋮ Systems of orthogonal polynomials arising from the modular \(j\)-function. ⋮ On certain generalized modular forms ⋮ Special values of modular functions on Hecke groups ⋮ Irreducibility of some Faber polynomials ⋮ On divisors of modular forms ⋮ Remarks on \(q\)-exponents of generalized modular functions ⋮ ZEROS OF WEAKLY HOLOMORPHIC MODULAR FORMS OF LEVEL 4 ⋮ Conjugacy growth series for finitary wreath products ⋮ Valence formulas for certain arithmetic groups and their applications ⋮ Some remarks on the \(q\)-exponents of generalized modular functions ⋮ Divisors of modular forms on \(\Gamma_{0}(4)\) ⋮ Poincaré series and the divisors of modular forms ⋮ Heegner zeros of theta functions ⋮ On the reciprocal of Klein's absolute \(j\)-invariant and sign changes ⋮ The action of the heat operator on Jacobi forms ⋮ The Hecke algebra action and the Rezk logarithm on Morava E-theory of height 2 ⋮ AN EXTENSION OF ROHRLICH’S THEOREM TO THE -FUNCTION ⋮ On sign changes of \(q\)-exponents of generalized modular functions ⋮ Infinite product exponents for modular forms ⋮ Transcendence of zeros of Jacobi forms ⋮ A CHARACTERIZATION OF THE MODULAR UNITS ⋮ ON FOURIER COEFFICIENTS OF MODULAR FORMS ⋮ Polynomial identities between Hecke eigenforms ⋮ Values of harmonic weak Maass forms on Hecke orbits ⋮ An algorithm for numerically inverting the modular \(j\)-function ⋮ FOURIER EXPANSIONS WITH MODULAR FORM COEFFICIENTS ⋮ \(p\)-adic liftings of the supersingular \(j\)-invariants and \(j\)-zeros of certain Eisenstein series ⋮ Semistable models for modular curves and power operations for Morava E-theories of height 2 ⋮ De Moivre and Bell polynomials ⋮ Some formulas for the coefficients of Drinfeld modular forms