The Elliptic Apostol-dedekind Sums Generate Odd Dedekind Symbols with Laurent Polynomial Reciprocity Laws

نویسنده

  • SHINJI FUKUHARA
چکیده

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 polynomial reciprocity laws. Our construction is based on Machide’s result [7] on his elliptic Dedekind-Rademacher sums. As an application of our results, we discover Eisenstein series identities which generalize certain formulas by Ramanujan[11], van der Pol [9], Rankin[12] and Skoruppa [14].

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تاریخ انتشار 2009