A class of conjectured series representations for .
A cubic analogue of the theta series.
A cubic analogue of the theta series. II.
A Cuspidal Class Number Formula for the Modular Curves X1(N).
A few remarks on automorphic functions.
A Modular Construction of Unramified p-Extension of Q (...).
A modular identity for the Ramanujan identity modulo 35.
A new proof of the reciprocity theorem for Dedekind sums.
A System of Free Generators for the Universal even Ordinary Z(2) Distribution on Q2k-Z2k .
An ...-Result for the Coefficients of Cusp Forms.
Analogs of Δ(z) for triangular Shimura curves
We construct analogs of the classical Δ-function for quotients of the upper half plane 𝓗 by certain arithmetic triangle groups Γ coming from quaternion division algebras B. We also establish a relative integrality result concerning modular functions of the form Δ(αz)/Δ(z) for α in B⁺. We give two explicit examples at the end.
Analyse spectrale et prolongement analytique : séries d’Eisenstein, fonctions et nombre de solutions d’équations diophantiennes
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
Arithmetic differential equations in several variables
We survey recent work on arithmetic analogues of ordinary and partial differential equations.
Arithmetic of the modular function
We find a generator of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.
Arithmétique de courbes modulaires
Arithmetisch ganze Differentiale der Modulfunktionenkörper 6. und 7. Stufe
Asymptotic formulae for partition ranks
Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.
Asymptotic Formulae for the Coefficients of a Class of Modular Forms.
Asymptotic formulas for the coefficients of certain automorphic functions
We derive asymptotic formulas for the coefficients of certain classes of weakly holomorphic Jacobi forms and weakly holomorphic modular forms (not necessarily of integral weight) without using the circle method. Then two applications of these formulas are given. Namely, we estimate the growth of the Fourier coefficients of two important weak Jacobi forms of index 1 and non-positive weights and obtain an asymptotic formula for the Fourier coefficients of the modular functions for all integers k,l...