Dedekind cotangent sums

By Matthias Beck. 2001

48 citations recorded by the source corpus.

Let a,a1,...,ad be positive integers, m1,...,md nonnegative integers, and z1,...,zd complex numbers. We study expressions of the form X k mod a d Y j=1 cot (mj) kaj a + z j . Here the sum is taken over all k mod a for which the summand is not singular. These Dedekind cotangent sums generalize and unify various arithmetic sums introduced by Dedekind, Rademacher, Apostol, Carlitz, Zagier, Berndt, Meyer, Sczech, and Dieter. Generalized Dedekind sums appear in various areas such as analytic and algebraic number theory, topology, algebraic and combinatorial geometry, and algorithmic complexity. We prove reciprocity laws, Petersson-Knopp identities, and computability statements for the Dedekind cotangent sums.

Subfields: Algebra and Number Theory, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/429b9d263fa1eace5ed122f9e4fbea3b3f929fdb

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In Algebra and Number Theory

1. Yilmaz Simsek
2. Taekyun Kim
3. Veli Kurt
4. Hari M. Srivastava
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In Statistics and Probability

1. Yilmaz Simsek
2. Taekyun Kim

Citations in the corpus

• Special functions related to Dedekind-type DC-sums and their applications (2009, background): “In the literature of the Dedekind sums, there are several generalizations of the Dedekind sums that involve higher order Bernoulli functions and Euler functions, the reader should look at [23], [1], [7]-[9], [19], [4], [5] and [36] for references and, see also the references cited in each of these e”