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![Correlations between ‖u-t‖2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Vert \textbf{u}-\textbf{t}\Vert ^2$$\end{document} and hStR(y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_{StR}(y)$$\end{document} 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}, where u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{u}$$\end{document} is the lattice point corresponding to y](publication/386435528/figure/fig4/AS:11431281314631918@1741490221168/Correlations-between-u-t2documentclass12ptminimal-usepackageamsmath.png)
Correlations between ‖u-t‖2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Vert \textbf{u}-\textbf{t}\Vert ^2$$\end{document} and hStR(y)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_{StR}(y)$$\end{document} 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}, where u\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{u}$$\end{document} is the lattice point corresponding to y
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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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