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On A Generalization of Hecke ϑ-Functions

On A Generalization of Hecke ϑ-Functions and the Analytic Proof of Higher Reciprocity Laws

✍ M.C. Berg 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 510 KB

In the 1920s Hecke posed the problem of providing the analytic proof of the reciprocity law for the \(m\) th power residue symbol, along the same lines as his proof of relative quadratic reciprocity. We show that a naive approach, based on a suggestive way of generalizing Hecke \(\vartheta\)-functio