{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T05:19:52Z","timestamp":1740028792963,"version":"3.37.3"},"reference-count":0,"publisher":"IOS Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"abstract":"<jats:p>Let &amp;chi; be an irreducible, smooth, projective curve of genus g &amp;ge; 2 defined over the complex field C. Then there is a covering &amp;pi; : &amp;chi; &amp;rarr; P1, where P1denotes the projective line. The problem of expressing branch points of the covering &amp;pi; in terms of the transcendentals (period matrix, thetanulls, e.g.) is classical. It goes back to Riemann, Jacobi, Picard and Rosenhein. Many mathematicians, including Picard and Thomae, have offered partial treatments for this problem. In this work, we address the problem for cyclic curves of genus 2, 3, and 4 and find relations among theta functions for curves with automorphisms. We consider curves of genus g &amp;gt; 1 admitting an automorphism &amp;sigma; such that &amp;chi;&amp;sigma;has genus zero and &amp;sigma; generates a normal subgroup of the automorphism group Aut(&amp;chi;) of &amp;chi;.<\/jats:p>","DOI":"10.3233\/978-1-60750-019-3-193","type":"book-chapter","created":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T19:11:46Z","timestamp":1739992306000},"source":"Crossref","is-referenced-by-count":0,"title":["Theta functions and algebraic curves with automorphisms"],"prefix":"10.3233","author":[{"family":"Shaska T.","sequence":"additional","affiliation":[]},{"family":"Wijesiri G.S.","sequence":"additional","affiliation":[]}],"member":"7437","container-title":["NATO Science for Peace and Security Series - D: Information and Communication Security","Algebraic Aspects of Digital Communications"],"original-title":[],"deposited":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T19:27:37Z","timestamp":1739993257000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospressISSNISBN&issn=1874-6268&volume=24&spage=193"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/978-1-60750-019-3-193","relation":{},"ISSN":["1874-6268"],"issn-type":[{"value":"1874-6268","type":"print"}],"subject":[],"published":{"date-parts":[[2009]]}}}