대한수학회논문집 (Communications of the Korean Mathematical Society)
- 제11권1호
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- Pages.57-62
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- 1996
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
Convergence and the Riemann hypothesis
초록
For $1 < p \leq 2$ it is shown that a certain sequence of functions converges to -1 in $L^{p-\varepsilon}(0, 1)$ for any small $\varepsilon > 0$ if and only if the Riemann zeta function satisfies $\zeta(s) \neq 0$ for $\sigma = Re s > 1/p$.