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Dedekind sums
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# Dedekind sums

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Published by Mathematical Association of America in [Washington] .
Written in English

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• Dedekind sums.

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Classifications The Physical Object Statement by Hans Rademacher and Emil Grosswald. Series Carus mathematical monographs -- no. 16. Contributions Grosswald, Emil. LC Classifications QA241 .R2 1972 Pagination xvi, 102 p. Number of Pages 102 Open Library OL17755205M

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Additional Physical Format: Online version: Rademacher, Hans, Dedekind sums. [Washington] Mathematical Association of America [] (OCoLC) Book Description: These notes from Hans Rademacher’s Hedrick Lectures have been gently polished and augmented by Emil Grosswald. While the topic itself is specialized, these sums are linked in diverse ways to many results in number theory, elliptical modular functions, and topology. Dedekind sums arose out of the study of elliptic functions and modular forms. They were iniially discovered by Dedekind but have since been studied for their many arithmetic properties. Much work has been done on Dedekind sums and in Rademacher and Grosswald released a book that summarised much of what was known, as well as providing a history of Dedekind sums. Richard Dedekind is the author of Essays on the Theory of Numbers ( avg rating, ratings, 10 reviews, published ), Theory Of Algebraic Integer /5.

Dedekind Sums Let ((x)):= (x−bxc− 1 2 if x /∈ Z, 0 if x ∈ Z, and deﬁne the Dedekind sum as s(a,b):= bX−1 k=1 ka b k b = 1 4b Xb−1 j=1 cot πja b cot πj b. Since their introduction by Dedekind in the ’s, these sums and their generalizations have appeared in various areas such as analyticFile Size: KB. The idea behind Dedekind cuts is to just work with the pairs (A,B), without direct reference to any real number. Basically, we just look at all the properties that (A x,B x) has and then make these “axioms” for what we mean by a Dedekind cut. 4 The Main Deﬁnition A Dedekind cut is a pair (A,B), where Aand Bare both subsets of rationals. Dedekind treated the property as a theorem, so it takes intellectual e ort for readers of Dedekind to recognized it as a good axiom Dedekind didn’t give the property a name Dedekind didn’t state the property in a succinct self-contained way (and it’s somewhat resistant to being stated in . Dedekind sums. [Washington]: Mathematical Association of America. Chicago / Turabian - Author Date Citation (style guide) Rademacher, Hans, and Emil. Grosswald. Dedekind Sums. [Washington]: Mathematical Association of America. Chicago / Turabian - Humanities Citation (style guide) Rademacher, Hans, and Emil. Grosswald.

Dedekind sums | Hans Rademacher, Emil Grosswald. | download | B–OK. Download books for free. Find books. Higher Dimensional Dedekind Sums bounded by a number depending only on n (3 for n = 2, as one sees from (2), 45 for n = 4, and so on). The plan of the paper is as follows. In the first section we treat the case n = 2, i.e. the classical Dedekind sum. This section serves to illus-. Dedekind’s deﬁnition of real numbers 3 3. Deﬁning arithmetic operations Let’s see if we can deﬁne addition, which we couldn’t do if we deﬁned a real number to be a decimal expansion. Suppose x and y are two real numbers. Deﬁne a set A to be the set of all rational numbers r + s with r in Ax and s in Ay. It may happen that the. In mathematics, Dedekind sums are certain sums of products of a sawtooth function, and are given by a function D of three integer variables. Dedekind introduced them to express the functional equation of the Dedekind eta function. They have subsequently been much studied in number theory, and have occurred in some problems of topology. Dedekind sums have a large number functional equations; this article lists only a small fraction of these. Dedekind .