Linked from

The 11 pages that link to Explicit formula, each with the reason it gives.

• Riemann zeta functionRelated: The Riemann explicit formula makes the influence of zeta zeros on prime distribution precise.

• Riemann hypothesisRelated: It translates zero locations into oscillations in the distribution of primes.

• Analytic number theoryRelated: It translates the locations of zeta zeros into fluctuations in prime counts.

• Geometric progressionRelated: For first term a and ratio r, it gives the nth term as a times r to the power n−1.

• Goldbach's conjectureRelated: Prime-distribution estimates inform analytic approaches to Goldbach, but do not yet close the proof gap.

• Generalized Riemann hypothesisRelated: It translates zero locations into precise information about arithmetic distributions.

• Integer sequenceRelated: It can specify each term directly as a function of its position.

• Linnik's theoremRelated: It translates zero information into estimates for primes in arithmetic progressions.

• Montgomery pair correlation conjectureRelated: It translates zero correlations into weighted prime correlations, where arithmetic structure may explain the prediction.