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- W2052099005 abstract "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." @default.
- W2052099005 created "2016-06-24" @default.
- W2052099005 creator A5007719593 @default.
- W2052099005 date "2003-01-01" @default.
- W2052099005 modified "2023-10-16" @default.
- W2052099005 title "Dedekind cotangent sums" @default.
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- W2052099005 doi "https://doi.org/10.4064/aa109-2-1" @default.
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