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The Epstein-type zeta function introduced by Davenport and Heilbronn (1936), a linear combination of two Dirichlet L-functions attached to the non-principal characters mod 5. It satisfies a Riemann-type functional equation yet has zeros off the critical line; claims about its construction, zeros, and role as the standard example that a functional equation alone does not force zeros onto the critic

The Davenport-Heilbronn function satisfies a Riemann-type functional equation yet has zeros off the critical line.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Number theory Riemann hypothesisimportance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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