Abstract
We prove a Voronoi–Oppenheim summation formula for divisor functions associated with Gaussian integers. This formula is a direct generalization of Oppenheim’s summation formula for classical divisor functions. To prove the formula we construct an Eisenstein series and study its properties. Our method of proof is similar to Beineke and Bump’s proof of the classical Oppenheim summation formula.
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The first author is supported in part at the Technion by a postdoctoral fellowship. The third author acknowledges the support of the National Science Foundation grant DMS-1601026.
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Banerjee, D., Baruch, E.M. & Bump, D. Voronoi summation formula for Gaussian integers. Ramanujan J 57, 253–274 (2022). https://doi.org/10.1007/s11139-020-00378-4
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DOI: https://doi.org/10.1007/s11139-020-00378-4