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 of functional equations; this article lists only a small fraction of these.
Dedekind sums were introduced by Richard Dedekind in a commentary on fragment XXVIII of Bernhard Riemann's collected papers.
mathematics, Dedekindsums are certain sums of products of a sawtooth function, and are given by a function D of three integer variables. Dedekind introduced...
Richard DedekindDedekind cut Dedekind domain Dedekind eta function Dedekind-infinite set Dedekind number Dedekind psi function DedekindsumDedekind zeta...
In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors...
number Dedekind's problem Dedekind–Peano axioms Dedekind psi function Dedekind ring DedekindsumDedekind valuation Dedekind zeta function Dedekind–Hasse...
In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane...
{\displaystyle A_{k}(n)=\sum _{0\leq m<k,\;(m,k)=1}e^{\pi i\left(s(m,k)-2nm/k\right)}.} and s ( m , k ) {\displaystyle s(m,k)} is the Dedekindsum. The multiplicative...
theory, a Dedekind group is a group G such that every subgroup of G is normal. All abelian groups are Dedekind groups. A non-abelian Dedekind group is...
Recurring decimal Cyclic number Farey sequence Ford circle Stern–Brocot tree Dedekindsum Egyptian fraction Montgomery reduction Modular exponentiation Linear...
ordered field that is Dedekind complete. Here, "completely characterized" means that there is a unique isomorphism between any two Dedekind complete ordered...
mathematics, the Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekind number M(n)...
In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζK(s), is a generalization of the Riemann zeta function (which...
the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers...
variable, and quantum theory. Most notably, he developed the theory of Dedekindsums. In 1937 Rademacher discovered an exact convergent series for the partition...
mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number 9045...
repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration...
about the transfer function of passive networks Reciprocity law for Dedekindsums Betti's theorem in linear elasticity Reciprocity (disambiguation) This...
Fourier series (/ˈfʊrieɪ, -iər/) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric...
domains. However, rings of algebraic integers satisfy the weaker property of Dedekind domains: ideals factor uniquely into prime ideals. Factorization may also...
mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence...
In number theory, the Dedekind psi function is the multiplicative function on the positive integers defined by ψ ( n ) = n ∏ p | n ( 1 + 1 p ) , {\displaystyle...
Frobenius reciprocity, from group representation theory Reciprocity law for Dedekindsums Stanley's reciprocity theorem, states that a certain functional equation...
set of real numbers is the Dedekind completion of the set of rational numbers. A real number is defined to be a Dedekind cut of rationals: a non-empty...
JSTOR 2313922. Kurt Girstmair; Girstmair, Kurt (2010). "Farey Sums and DedekindSums". The American Mathematical Monthly. 117 (1): 72–78. doi:10.4169/000298910X475005...
of representations of n as a sum of two squares of nonnegative integers. So one can compute the residue of the Dedekind zeta function at s = 1 by computing...
and although Dedekind himself referred to the book throughout his life as Dirichlet's, the book itself was entirely written by Dedekind, for the most...
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