q-Identities for Maass waveforms (Corrigendum).
Quadratic forms and a product-to-sum formula
Rademacher-Carlitz polynomials
We introduce and study the Rademacher-Carlitz polynomial where , s,t ∈ ℝ, and u and v are variables. These polynomials generalize and unify various Dedekind-like sums and polynomials; most naturally, one may view R(u,v,s,t,a,b) as a polynomial analogue (in the sense of Carlitz) of the Dedekind-Rademacher sum , which appears in various number-theoretic, combinatorial, geometric, and computational contexts. Our results come in three flavors: we prove a reciprocity theorem for Rademacher-Carlitz...
Ramanujan's class invariants, Kronecker's limit formula and modular equations (III)
Ramanujan's identities for eta-functions.
Reciprocity formulae for general Dedekind-Rademacher sums
Reciprocity formulae for general multiple Dedekind-Rademacher sums and enumeration of lattice points
Reciprocity laws for generalized higher dimensional Dedekind sums
We define a class of generalized Dedekind sums and prove a family of reciprocity laws for them. These sums and laws generalize those of Zagier [6]. The method is based on that of Solomon [5].
Series and iterations for 1/π
Some eta-identities arising from theta series.
Some identities for multiple Dedekind sums attached to Dirichlet characters
Some remarks on certain generalized Dedekind sums
Some theorems on the explicit evaluation of Ramanujan's theta-functions.
Sommes de Dedekind elliptiques et formes de Jacobi
À partir des formes de Jacobi , on construit une somme de Dedekind elliptique. On obtient ainsi un analogue elliptique aux sommes multiples de Dedekind construites à partir des fonctions cotangentes, étudiées par D. Zagier. En outre, on établit une loi de réciprocité satisfaite par ces nouvelles sommes. Par une procédure de limite, on peut retrouver la loi de réciprocité remplie par les sommes multiples de Dedekind classiques. D’autre part, en les spécialisant en des paramètres de points de 2- division,...
The construction of modular forms as products of transforms of the Dedekind eta function
The Ehrhart polynomial of a lattice -simplex.
The Eisenstein family for the modular group along closed geodescis.
The hybrid mean value of Dedekind sums and two-term exponential sums
In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and asymptotic formula for it.
The reciprocity theorem for Dedekind-Rademacher sums
Toric varieties, lattice points and Dedekind sums.