The elliptic Apostol–Dedekind sums generate odd Dedekind symbols with Laurent polynomial reciprocity laws
نویسندگان
چکیده
منابع مشابه
The 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...
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We introduce an elliptic analogue of the Apostol sums, which we call elliptic Apostol sums. These sums are defined by means of certain elliptic functions with a complex parameter τ having positive imaginary part. When τ → i∞, these elliptic Apostol sums represent the well-known Apostol generalized Dedekind sums. Also these elliptic Apostol sums are modular forms in the variable τ . We obtain a ...
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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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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2009
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-009-0416-7