Pascal's triangle and the Fibonacci sequence also seem inexplicably widespread in nature. Then there's the Riemann zeta function, a deceptively straightforward function that has perplexed ...

Parallel investigations have probed the behaviour of the Riemann zeta-function within short intervals ... as those based on shifts aligned with sequences of Gram points—offer promising ...

Forbes contributors publish independent expert analyses and insights. So what? Riemann was interested in the distribution of prime numbers and he discovered a formula for the number of primes less ...

these inputs are the “nontrivial zeros” of the zeta function. Riemann discovered a formula for calculating the number of primes up to any given cutoff by summing over a sequence of these zeros.

The Riemann zeta function is one of the most central functions in number ... There’s no general recipe for constructing a suitable sequence of fractions. Sometimes, a good sequence will fall into your ...

The value of the zeta function ζ(3) had been an open question for more than 200 years. The brilliant Swiss mathematician Leonhard Euler had cut his teeth on it and failed to solve it. Now Apéry ...

He dealt with a specific function, the so-called zeta function ζ(s), an infinitely long sum that adds the reciprocal values of natural numbers that are raised to the power of s: Even before ...

The Riemann hypothesis itself states that the zeros of a particular function, known as the Riemann zeta function, all lie along a specific line in what is known as the complexplane. The zeros of this ...