It is an important open question whether all of its nontrivial zeroes have real part one-half.
Physicists use this mathematical object to regularize divergent sums, setting its value for argument 1-k to be minus the kth Bernoulli number over k. By Voronin's theorem, this function exhibits universality, so that it can approximate any non-zero holomorphic function arbitrarily closely inside its critical strip. A generalization of one conjecture about this function is stated in terms of Dirichlet L-functions. For a complex number s with real part greater than 1, this function equals the sum of "n to the negative s" taken over all positive integers n. It is an important open question whether all of its nontrivial zeroes have real part one-half. For 10 points, name this function that is the subject of the Riemann hypothesis.
Physicists use this mathematical object to regularize divergent sums, setting its value for argument 1-k to be minus the kth Bernoulli number over k.
Riemann zeta function