Borwein, Peter; Fee, Greg; Ferguson, Ron; van der Waall, Alexa Zeros of partial sums of the Riemann zeta function. (English) Zbl 1219.11126 Exp. Math. 16, No. 1, 21-39 (2007). Summary: The semiperiodic behavior of the zeta function \(\zeta(s)\) and its partial sums \(\zeta_N(s)\) as a function of the imaginary coordinate has been long established. In fact, the zeros of a \(\zeta_N(s)\), when reduced into imaginary periods derived from primes less than or equal to \(N\), establish regular patterns. We show that these zeros can be embedded as a dense set in the period of a surface in \(\mathbb R^{k+1}\), where \(k\) is the number of primes in the expansion. This enables us, for example, to establish the lower bound for the real parts of zeros of \(\zeta_N(s)\) for prime \(N\) and justifies the use of methods of calculus to find expressions for the bounding curves for sets of reduced zeros in \(\mathbb C\). Cited in 14 Documents MSC: 11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses 11Y35 Analytic computations × Cite Format Result Cite Review PDF Full Text: DOI Euclid