Quadratic class numbers and character sums

Research output: Contribution to journalArticle (Academic Journal)peer-review

17 Citations (Scopus)


We present an algorithm for computing the class number of the quadratic number field of discriminant d. The algorithm terminates unconditionally with the correct answer and, under the GRH, executes in O-epsilon(vertical bar d vertical bar(1/4+epsilon)) steps. The technique used combines algebraic methods with Burgess' theorem on character sums to estimate L( 1, chi(d)). We give an explicit version of Burgess' theorem valid for prime discriminants and, as an application, we compute the class number of a 32-digit discriminant.
Translated title of the contributionQuadratic class numbers and character sums
Original languageEnglish
Pages (from-to)1481 - 1492
Number of pages12
JournalMathematics of Computation
Volume75 (255)
Publication statusPublished - Jul 2006

Bibliographical note

Publisher: American Mathematical Society
Other identifier: IDS number 065TF


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