1.0Arbeitsgemeinschaft der Universitätsverlagehttps://universitaetsverlage.euXMLRPChttps://universitaetsverlage.eu/author/xmlrpc/rich600338<blockquote class="wp-embedded-content"><a href="https://universitaetsverlage.eu/bucher-e-books/titel/on-length-spectra-of-lattices/">On length spectra of lattices</a></blockquote> <script type='text/javascript'> <!--//--><![CDATA[//><!-- /*! This file is auto-generated */ !function(d,l){"use strict";var e=!1,o=!1;if(l.querySelector)if(d.addEventListener)e=!0;if(d.wp=d.wp||{},!d.wp.receiveEmbedMessage)if(d.wp.receiveEmbedMessage=function(e){var t=e.data;if(t)if(t.secret||t.message||t.value)if(!/[^a-zA-Z0-9]/.test(t.secret)){var r,a,i,s,n,o=l.querySelectorAll('iframe[data-secret="'+t.secret+'"]'),c=l.querySelectorAll('blockquote[data-secret="'+t.secret+'"]');for(r=0;r<c.length;r++)c[r].style.display="none";for(r=0;r<o.length;r++)if(a=o[r],e.source===a.contentWindow){if(a.removeAttribute("style"),"height"===t.message){if(1e3<(i=parseInt(t.value,10)))i=1e3;else if(~~i<200)i=200;a.height=i}if("link"===t.message)if(s=l.createElement("a"),n=l.createElement("a"),s.href=a.getAttribute("src"),n.href=t.value,n.host===s.host)if(l.activeElement===a)d.top.location.href=t.value}}},e)d.addEventListener("message",d.wp.receiveEmbedMessage,!1),l.addEventListener("DOMContentLoaded",t,!1),d.addEventListener("load",t,!1);function t(){if(!o){o=!0;var e,t,r,a,i=-1!==navigator.appVersion.indexOf("MSIE 10"),s=!!navigator.userAgent.match(/Trident.*rv:11\./),n=l.querySelectorAll("iframe.wp-embedded-content");for(t=0;t<n.length;t++){if(!(r=n[t]).getAttribute("data-secret"))a=Math.random().toString(36).substr(2,10),r.src+="#?secret="+a,r.setAttribute("data-secret",a);if(i||s)(e=r.cloneNode(!0)).removeAttribute("security"),r.parentNode.replaceChild(e,r)}}}}(window,document); //--><!]]> </script><iframe sandbox="allow-scripts" security="restricted" src="https://universitaetsverlage.eu/bucher-e-books/titel/on-length-spectra-of-lattices/embed/" width="600" height="338" title="„On length spectra of lattices“ — Arbeitsgemeinschaft der Universitätsverlage" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" class="wp-embedded-content"></iframe>https://universitaetsverlage.eu/wp-content/uploads/asolmerce/image-9783866445840.jpg452640The aim of this work is to study Schmutz Schaller"s conjecture that in dimensions 2 to 8 the lattices with the best sphere packings have maximal lengths. This means that the distinct norms which occur in these lattices are greater than those of any other lattice in the same dimension with the same covolume. Although the statement holds asymptotically we explicitly present a counter-example. However, it seems that there is nothing but this exception.