New versions of the Nyman-Beurling criterion for the Riemann hypothesis
Let ρ(x)=x−[x], χ=χ(0,1), λ(x)=χ(x)logx, and M(x)=ΣK≤x μ(k), where μ is the Möbius function. Norms are in Lp(0,∞), 1<p<∞. For M1(θ)=M(1/θ) it is noted that ξ(s)≠0 in ℜs>1/p is equivalent to ‖M1‖r<∞ for all r∈(1,p). The space ℬ is the linear space generated by the functions x↦ρ(θ/x) with...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202013248 |
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