In number theory and harmonic analysis, the Landsberg–Schaar relation (or identity) is the following equation, which is valid for arbitrary positive integers p and q: Although both sides are mere finite sums, no proof by entirely finite methods has yet been found. The standard way to prove it is to put , where in this identity due to Jacobi (which is essentially just a special case of the Poisson summation formula in classical harmonic analysis): and then let If we let q = 1, the identity reduces to a formula for the quadratic Gauss sum modulo p.

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• In number theory and harmonic analysis, the Landsberg–Schaar relation (or identity) is the following equation, which is valid for arbitrary positive integers p and q: Although both sides are mere finite sums, no proof by entirely finite methods has yet been found. The standard way to prove it is to put , where in this identity due to Jacobi (which is essentially just a special case of the Poisson summation formula in classical harmonic analysis): and then let If we let q = 1, the identity reduces to a formula for the quadratic Gauss sum modulo p. The Landsberg–Schaar identity can be rephrased more symmetrically as provided that we add the hypothesis that pq is an even number. (en)
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• In number theory and harmonic analysis, the Landsberg–Schaar relation (or identity) is the following equation, which is valid for arbitrary positive integers p and q: Although both sides are mere finite sums, no proof by entirely finite methods has yet been found. The standard way to prove it is to put , where in this identity due to Jacobi (which is essentially just a special case of the Poisson summation formula in classical harmonic analysis): and then let If we let q = 1, the identity reduces to a formula for the quadratic Gauss sum modulo p. (en)
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• Landsberg–Schaar relation (en)
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