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The Riemann zeta function ζ(s): its Dirichlet series Σ n^(−s), the Euler product over primes ∏_p (1 − p^(−s))^(−1) valid for Re(s) > 1, analytic continuation, functional equation, special values, zeros, and other properties. Claims about the conjecture that its non-trivial zeros lie on the critical line belong to the Riemann hypothesis tag; claims about other zeta and L-function analogues belong t

Riemann's explicit formula expresses the prime-counting function as a sum over the non-trivial zeros of the zeta function.

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 Prime number theoremimportance · settledImportance 0.12, 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 →

The prime number theorem is equivalent to the non-vanishing of the Riemann zeta function on the line with real part 1.

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 →Prime number theorem Number theoryimportance · settledImportance 0.12, 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 →

The Riemann zeta function equals the Euler product over all primes of 1/(1 − p^(−s)) for real part of s greater than 1.

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 theoryimportance · settledImportance 0.12, 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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