A density result for elliptic Dedekind sums
A function on the upper half space which is analogous to the imaginary part of log ... (z).
A generalization of Rademacher's reciprocity law
We generalize Rademacher's reciprocity formula for the Dedekind sum to a family of cotangent sums. One of the sums in this family is strictly related to the Vasyunin sum, a function defined on the rationals that is relevant to the Nyman-Beurling-Báez-Duarte approach to the Riemann hypothesis.
A generalization of the reciprocity law of multiple Dedekind sums
Various multiple Dedekind sums were introduced by B.C.Berndt, L.Carlitz, S.Egami, D.Zagier and A.Bayad.In this paper, noticing the Jacobi form in Bayad [4], the cotangent function in Zagier [23], Egami’s result on cotangent functions [14] and their reciprocity laws, we study a special case of the Jacobi forms in Bayad [4] and deduce a generalization of Egami’s result on cotangent functions and a generalization of Zagier’s result. Further, we consider their reciprocity laws.
A hybrid mean value involving two-term exponential sums and polynomial character sums
Let be a positive integer. For any integers and , the two-term exponential sum is defined by , where . In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.
A hybrid mean value of the Dedekind sums
The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.
A hybrid mean value related to Dedekind sums
The main purpose of this paper is to study a hybrid mean value problem related to the Dedekind sums by using estimates of character sums and analytic methods.
A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity
In the transformation formulas for the logarithms of the classical theta-functions, certain sums arise that are analogous to the Dedekind sums in the transformation of the logarithm of the eta-function. A new reciprocity law is established for one of these analogous sums and then applied to prove the law of quadratic reciprocity.
A reciprocity theorem and a three-term relation for generalized Dedekind-Rademacher sums
A sum analogous to Dedekind sums and its hybrid mean value formula
An elliptic analogue of the multiple Dedekind sums
An identity involving Dedekind sums and generalized Kloosterman sums
The various properties of classical Dedekind sums have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums . The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of...
Asymptotic expansions of certain q-series and a formula of Ramanujan for specific values of the Riemann zeta function
Asymptotic formulas and generalized Dedekind sums.
Bernoulli-Dedekind sums
Cocycles d'Euler et de Maslov.
Concernant la relation de distribution satisfaite par la fonction ...associé à un réseau complexe.
Constructing elliptic curves over finite fields using double eta-quotients
We examine a class of modular functions for whose values generate ring class fields of imaginary quadratic orders. This fact leads to a new algorithm for constructing elliptic curves with complex multiplication. The difficulties arising when the genus of is not zero are overcome by computing certain modular polynomials.Being a product of four -functions, the proposed modular functions can be viewed as a natural generalisation of the functions examined by Weber and usually employed to construct...
Continued fractions and density results for Dedekind sums.
Das Verhalten der Dedekindschen Funktion ...(...) unter Modulsubstitutionen.