On the Dedekind sums and its new reciprocity formula
نویسندگان
چکیده
منابع مشابه
On 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.
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In this paper, we introduce a new sum analogous to Gauss sum, then we use the properties of the classical Gauss sums and analytic method to study the hybrid mean value problem involving this new sums and Dedekind sums, and give an interesting identity for it.
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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...
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ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2018
ISSN: 1787-2405,1787-2413
DOI: 10.18514/mmn.2018.1664