{"title":"Jun-Ichi Igusa","description":null,"products":[{"product_id":"theta-functions-book-jun-ichi-igusa-9783642653179","title":"Theta Functions","description":"The theory of theta functions has a long history; for this, we refer A. Krazer and W. Wirtinger the reader to an encyclopedia article by (\"Sources\" [9]). We shall restrict ourselves to postwar, i. e. , after 1945, periods. Around 1948\/49, F. Conforto, c. L. Siegel, A. Well reconsidered the main existence theorems of theta functions and found natural proofs for them. These are contained in Conforto: Abelsche Funktionen und algebraische Geometrie, Springer (1956); Siegel: Analytic functions of several complex variables, Lect. Notes, I. A. S. (1948\/49); Well: Theoremes fondamentaux de la theorie des fonctions theta, Sem. Bourbaki, No. 16 (1949). The complete account of Weil's method appeared in his book of 1958 [20]. The next important achievement was the theory of compacti- fication of the quotient variety of Siegel's upper-half space by a modular group. There are many ways to compactify the quotient variety; we are talking about what might be called a standard compactification. Such a compactification was obtained first as a Hausdorff space by I. Satake in \"On the compactification of the Siegel space\", J. Ind. Math. Soc. 20, 259-281 (1956), and as a normal projective variety by W.\nL. Baily in 1958 [1]. In 1957\/58, H. Cartan took up this theory in his seminar [3]; it was shown that the graded ring of modular forms relative to the given modular group is a normal integral domain which is finitely generated over C.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52665553355025,"sku":"NLS9783642653179","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783642653179.jpg?v=1785999609"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-jun-ichi-igusa.oembed","provider":"World of Books ","version":"1.0","type":"link"}