منابع مشابه
The Pick Theorem and the Proof of the Reciprocity Law for Dedekind Sums
This paper is to provide some new generalizations of the Pick Theorem. We first derive a point-set version of the Pick Theorem for an arbitrary bounded lattice polyhedron. Then, we use the idea of a weight function of [2] to obtain a weighted version. Other Pick type theorems known to the author for the integral lattice Z2 are reduced to some special cases of this generalization. Finally, using...
متن کاملOn Reciprocity Formulas for Apostol’s Dedekind Sums and Their Analogues
Using the Euler-MacLaurin summation formula, we give alternative proofs for the reciprocity formulas of Apostol’s Dedekind sums and generalized Hardy-Berndt sums s3,p(b, c) and s4,p(b, c). We also obtain an integral representation for each sum.
متن کاملA 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 a...
متن کاملThe Elliptic Apostol-dedekind Sums Generate Odd Dedekind Symbols with Laurent Polynomial Reciprocity Laws
Abstract. Dedekind symbols are generalizations of the classical Dedekind sums (symbols). There is a natural isomorphism between the space of Dedekind symbols with Laurent polynomial reciprocity laws and the space of modular forms. We will define a new elliptic analogue of the Apostol-Dedekind sums. Then we will show that the newly defined sums generate all odd Dedekind symbols with Laurent poly...
متن کاملM ay 2 00 3 The Reciprocity Law for Dedekind Sums via the constant Ehrhart coefficient
These sums appear in various branches of mathematics: Number Theory, Algebraic Geometry, and Topology; they have consequently been studied extensively in various contexts. These include the quadratic reciprocity law ([13]), random number generators ([12]), group actions on complex manifolds ([9]), and lattice point problems ([14], [5]). Dedekind was the first to show the following reciprocity l...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1953
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1953.3.523