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![Profile of a 1-round BKZ-84 reduced basis of the Mertens lattice for N=120\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=120$$\end{document}, ν=130\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu = 130$$\end{document}, νy=100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu _y = 100$$\end{document}, νt=15\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu _t = 15$$\end{document}, and α∗=αexp(-1.5·10-6γ2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^* = \alpha \exp (-1.5 \cdot 10^{-6}\gamma ^2)$$\end{document}](publication/386435528/figure/fig2/AS:11431281314631917@1741490220626/Profile-of-a-1-round-BKZ-84-reduced-basis-of-the-Mertens-lattice-for.png)
Profile of a 1-round BKZ-84 reduced basis of the Mertens lattice for N=120\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=120$$\end{document}, ν=130\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu = 130$$\end{document}, νy=100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu _y = 100$$\end{document}, νt=15\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu _t = 15$$\end{document}, and α∗=αexp(-1.5·10-6γ2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ^* = \alpha \exp (-1.5 \cdot 10^{-6}\gamma ^2)$$\end{document}
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![Correlations between hStR(y)\documentclass[12pt]{minimal}...](publication/386435528/figure/fig3/AS:11431281314603541@1741490220806/Correlations-between-hStRydocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Correlations between ‖u-t‖2\documentclass[12pt]{minimal}...](publication/386435528/figure/fig4/AS:11431281314631918@1741490221168/Correlations-between-u-t2documentclass12ptminimal-usepackageamsmath_Q320.jpg)
We use state-of-art lattice algorithms to improve the upper bound on the lowest counterexample to the Mertens conjecture to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen...
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