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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Modular unit</span></span>
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<p>In <a href="Mathematics" title="Mathematics">mathematics</a>, <b>modular units</b> are certain units of <a href="Ring_(mathematics)" title="Ring (mathematics)">rings</a> of integers of fields of <a href="Modular_function" class="mw-redirect" title="Modular function">modular functions</a>, introduced by <a href="Daniel_Kubert" title="Daniel Kubert">Kubert</a> and <a href="Serge_Lang" title="Serge Lang"> Lang</a> (<a href="#CITEREFKubertLang1975">1975</a>). They are functions whose <a href="Zero_of_a_function" title="Zero of a function">zeroes</a> and <a href="Pole_(complex_analysis)" class="mw-redirect" title="Pole (complex analysis)">poles</a> are confined to the cusps (images of infinity).
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<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Cyclotomic_unit" title="Cyclotomic unit">Cyclotomic unit</a></li>
<li><a href="Elliptic_unit" title="Elliptic unit">Elliptic unit</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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</style><cite id="CITEREFKubertLang1981" class="citation cs2"><a href="Daniel_Kubert" title="Daniel Kubert">Kubert, Daniel S.</a>; <a href="Serge_Lang" title="Serge Lang">Lang, Serge</a> (1981), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=BwwzmZjjVdgC"><i>Modular units</i></a>, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 244, Berlin, New York: <a href="Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer-Verlag</a>, <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-387-90517-4</bdi>, <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0648603">0648603</a>, <a href="Zbl_(identifier)" class="mw-redirect" title="Zbl (identifier)">Zbl</a> <a rel="nofollow" class="external text" href="https://zbmath.org/?format=complete&q=an:0492.12002">0492.12002</a></cite></li>
<li><cite id="CITEREFKubertLang1975" class="citation cs2"><a href="Daniel_Kubert" title="Daniel Kubert">Kubert, Daniel S.</a>; <a href="Serge_Lang" title="Serge Lang">Lang, Serge</a> (1975), "Units in the modular function field. I", <i><a href="Mathematische_Annalen" title="Mathematische Annalen">Mathematische Annalen</a></i>, <b>218</b> (1): <span class="nowrap">67–</span>96, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01350068">10.1007/BF01350068</a>, <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0025-5831">0025-5831</a>, <a href="MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0437496">0437496</a>, <a href="Zbl_(identifier)" class="mw-redirect" title="Zbl (identifier)">Zbl</a> <a rel="nofollow" class="external text" href="https://zbmath.org/?format=complete&q=an:0311.14005">0311.14005</a></cite></li></ul>
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