Add to ORKGUsing analytic functional equations, Berndt derived three reciprocity laws connecting five arithmetical sums analogous to Dedekind sums. This paper gives elementary proofs of all three reciprocity laws and obtains them all from a common source, a polynomial reciprocity formula of L. Carlitz
AbstractAn elementary proof is given of the Hasse-Weil theorem about the number of solutions of the ...
AbstractAs an extension of the Dirichlet divisor problem, S. Chowla and H. Walum conjectured that, a...
AbstractWe give a p-adic proof of a certain new relation between the Bernoulli numbers Bk, similar t...
AbstractIn this paper, we study on two subjects. We first construct degenerate analogues of Dedekind...
We propose a certain formula of Dedekind sum by using two mutually distinct methods. The one is an e...
AbstractIn this note we present a short and elementary proof of Heckeʼs reciprocity law for Hecke–Ga...
Using analytic functional equations, Berndt derived three reciprocity laws connecting five arithmeti...
AbstractThe well-known law of quadratic reciprocity has over 150 proofs in print. We establish a rel...
AbstractThe classical Dedekind sums were found in transformation formulae of η-functions. It is know...
AbstractIn this paper derivatives of Dedekind sums are defined, and their reciprocity laws are prove...
We prove that the reciprocal sum $S_k(x)$ of the least common multiple of $k\geq 3$ positive integer...
AbstractIn this paper we give a simple proof for the reciprocity formula for the generalized Dedekin...
AbstractWe prove a reciprocity formula between Gauss sums that is used in the computation of certain...
AbstractTextIn this paper we investigate higher order dimensional Dedekind–Rademacher sums given by ...
AbstractA necessary and sufficient condition is given for a positive integer to appear as the denomi...
AbstractAn elementary proof is given of the Hasse-Weil theorem about the number of solutions of the ...
AbstractAs an extension of the Dirichlet divisor problem, S. Chowla and H. Walum conjectured that, a...
AbstractWe give a p-adic proof of a certain new relation between the Bernoulli numbers Bk, similar t...
AbstractIn this paper, we study on two subjects. We first construct degenerate analogues of Dedekind...
We propose a certain formula of Dedekind sum by using two mutually distinct methods. The one is an e...
AbstractIn this note we present a short and elementary proof of Heckeʼs reciprocity law for Hecke–Ga...
Using analytic functional equations, Berndt derived three reciprocity laws connecting five arithmeti...
AbstractThe well-known law of quadratic reciprocity has over 150 proofs in print. We establish a rel...
AbstractThe classical Dedekind sums were found in transformation formulae of η-functions. It is know...
AbstractIn this paper derivatives of Dedekind sums are defined, and their reciprocity laws are prove...
We prove that the reciprocal sum $S_k(x)$ of the least common multiple of $k\geq 3$ positive integer...
AbstractIn this paper we give a simple proof for the reciprocity formula for the generalized Dedekin...
AbstractWe prove a reciprocity formula between Gauss sums that is used in the computation of certain...
AbstractTextIn this paper we investigate higher order dimensional Dedekind–Rademacher sums given by ...
AbstractA necessary and sufficient condition is given for a positive integer to appear as the denomi...
AbstractAn elementary proof is given of the Hasse-Weil theorem about the number of solutions of the ...
AbstractAs an extension of the Dirichlet divisor problem, S. Chowla and H. Walum conjectured that, a...
AbstractWe give a p-adic proof of a certain new relation between the Bernoulli numbers Bk, similar t...