On the orthogonality of Atkin-like polynomials and orthogonal polynomial expansion of generalized Faber polynomials
DOI10.1007/s11139-024-00861-2MaRDI QIDQ6579287
Publication date: 25 July 2024
Published in: The Ramanujan Journal (Search for Journal in Brave)
orthogonal polynomialshypergeometric seriesgeneralized Faber polynomialsextremal quasimodular formsAtkin polynomials
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11) Classical hypergeometric functions, ({}_2F_1) (33C05) Hecke-Petersson operators, differential operators (one variable) (11F25)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the Atkin polynomials
- The Jack Daniels problem
- On the zeros and coefficients of certain weakly holomorphic modular forms
- On modular solutions of certain meromorphic modular differential equations
- Classical automorphic forms and hypergeometric functions
- Automorphic forms with singularities on Grassmannians
- Finite perturbations of orthogonal polynomials
- Lattices and strings
- Rational spectral transformations and orthogonal polynomials
- On modular forms arising from a differential equation of hypergeometric type
- Systems of orthogonal polynomials arising from the modular \(j\)-function.
- Products of generalized hypergeometric series.
- Die elliptischen Funktionen und ihre Anwendungen. Erster Teil: Die funktionentheoretischen und analytischen Grundlagen.
- On the representation of certain asymptotic series as convergent continued fractions.
- Ueber die Transformation der elliptischen Functionen und die Auflösung der Gleichungen fünften Grades.
- Manifold ways to Darboux-Halphen system
- Monstrous moonshine and monstrous Lie superalgebras
- Arithmetic properties of mirror map and quantum coupling
- Quasi-modular forms attached to elliptic curves. I
- The number of linear factors of supersingular polynomials and sporadic simple groups
- Regularized inner products of modular functions
- Hypergeometric series, modular linear differential equations and vector-valued modular forms
- The Fourier series and the functional equation of the absolute modular invariant \(J(\tau)\).
- The Fourier coefficients of the modular invariant \(J(\tau)\).
- The Atkin orthogonal polynomials for the Fricke groups of levels 5 and 7
- Ramanujan's Theta Functions
- Elliptic Modular Forms and Their Applications
- Logarithmic vector-valued modular forms
- THE ATKIN ORTHOGONAL POLYNOMIALS FOR THE LOW-LEVEL FRICKE GROUPS AND THEIR APPLICATION
- ON EXTREMAL QUASIMODULAR FORMS
- Regularized Inner Products and Errors of Modularity
- A generalization of a theorem of Rankin and Swinnerton-Dyer on zeros of modular forms
- Quasimodular forms as solutions of modular differential equations
- Supersingular conjectures for the Fricke group
This page was built for publication: On the orthogonality of Atkin-like polynomials and orthogonal polynomial expansion of generalized Faber polynomials