2009/07/23 by Shinji Fukuhara, Fukuhara, Shinji
Mathematics · #11F11 #11F20 #33E05 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F11 #msc:11F20 #msc:33E05
paper · pdf · doi:10.48550/arxiv.0907.4058
AMS-LaTeX, 21 pages
arxiv created 2009/07/23 · openalex publication_date 2009/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 on his elliptic Dedekind-Rademacher sums. As an application of our results, we discover Eisenstein series identities which generalize certain formulas by Ramanujan, van der Pol, Rankin and Skoruppa.