Add to ORKGWe propose a certain formula of Dedekind sum by using two mutually distinct methods. The one is an elementary number theoretic method and the other is a geometric method. Moreover, we re-prove the reciprocity law by the formula
AbstractThe main purpose of this paper is to prove a conjecture of the Euler numbers and its general...
AbstractAs a generalization of Calkin's identity and its alternating form, we compute a kind of bino...
AbstractWe consider some parametrized classes of multiple sums first studied by Euler. Identities be...
AbstractWe define a Dedekind symbol associated with a J-form (J-forms generalize the usual Jacobi fo...
AbstractIn this paper derivatives of Dedekind sums are defined, and their reciprocity laws are prove...
Using analytic functional equations, Berndt derived three reciprocity laws connecting five arithmeti...
AbstractThe classical Dedekind sums were found in transformation formulae of η-functions. It is know...
AbstractIn this paper, we study on two subjects. We first construct degenerate analogues of Dedekind...
AbstractThe homogeneous Dedekind sum is defined by[formula]This paper shows that[formula]It is the g...
AbstractTextIn this paper we investigate higher order dimensional Dedekind–Rademacher sums given by ...
AbstractIn this note we present a short and elementary proof of Heckeʼs reciprocity law for Hecke–Ga...
AbstractThe well-known law of quadratic reciprocity has over 150 proofs in print. We establish a rel...
AbstractLet q be an odd positive integer and let a be an integer coprime to q. For each integer b co...
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theor...
AbstractIn this paper, we use the properties of Gauss sums, primitive characters and the mean value ...
AbstractThe main purpose of this paper is to prove a conjecture of the Euler numbers and its general...
AbstractAs a generalization of Calkin's identity and its alternating form, we compute a kind of bino...
AbstractWe consider some parametrized classes of multiple sums first studied by Euler. Identities be...
AbstractWe define a Dedekind symbol associated with a J-form (J-forms generalize the usual Jacobi fo...
AbstractIn this paper derivatives of Dedekind sums are defined, and their reciprocity laws are prove...
Using analytic functional equations, Berndt derived three reciprocity laws connecting five arithmeti...
AbstractThe classical Dedekind sums were found in transformation formulae of η-functions. It is know...
AbstractIn this paper, we study on two subjects. We first construct degenerate analogues of Dedekind...
AbstractThe homogeneous Dedekind sum is defined by[formula]This paper shows that[formula]It is the g...
AbstractTextIn this paper we investigate higher order dimensional Dedekind–Rademacher sums given by ...
AbstractIn this note we present a short and elementary proof of Heckeʼs reciprocity law for Hecke–Ga...
AbstractThe well-known law of quadratic reciprocity has over 150 proofs in print. We establish a rel...
AbstractLet q be an odd positive integer and let a be an integer coprime to q. For each integer b co...
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theor...
AbstractIn this paper, we use the properties of Gauss sums, primitive characters and the mean value ...
AbstractThe main purpose of this paper is to prove a conjecture of the Euler numbers and its general...
AbstractAs a generalization of Calkin's identity and its alternating form, we compute a kind of bino...
AbstractWe consider some parametrized classes of multiple sums first studied by Euler. Identities be...