Modular Units

·
· Grundlehren der mathematischen Wissenschaften 第 244 冊 · Springer Science & Business Media
電子書
360
頁數
評分和評論未經驗證 瞭解詳情

關於這本電子書

In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Let i) be the upper half plane, and N a positive integer. Let r(N) be the subgroup of SL (Z) consisting of those matrices == 1 mod N. Then r(N)\i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N). The affine ring of regular functions on yeN) over C is the integral closure of C[j] in the function field of X(N) over C. Here j is the classical modular function. However, for arithmetic applications, one considers the curve as defined over the cyclotomic field Q(JlN) of N-th roots of unity, and one takes the integral closure either of Q[j] or Z[j], depending on how much arithmetic one wants to throw in. The units in these rings consist of those modular functions which have no zeros or poles in the upper half plane. The points of X(N) which lie at infinity, that is which do not correspond to points on the above affine set, are called the cusps, because of the way they look in a fundamental domain in the upper half plane. They generate a subgroup of the divisor class group, which turns out to be finite, and is called the cuspidal divisor class group.

為這本電子書評分

請分享你的寶貴意見。

閱讀資訊

智能手機和平板電腦
請安裝 Android 版iPad/iPhone 版「Google Play 圖書」應用程式。這個應用程式會自動與你的帳戶保持同步,讓你隨時隨地上網或離線閱讀。
手提電腦和電腦
你可以使用電腦的網絡瀏覽器聆聽在 Google Play 上購買的有聲書。
電子書閱讀器及其他裝置
如要在 Kobo 等電子墨水裝置上閱覽書籍,你需要下載檔案並傳輸到你的裝置。請按照說明中心的詳細指示,將檔案傳輸到支援的電子書閱讀器。