TWISTED QUADRATIC MOMENTS FOR DIRICHLET L-FUNCTIONS
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Given c, a positive integer, we set M(f, c) := 2/Φ(f) ∑ χ∈X− f χ(c)|L(1, χ)|2, where X− f is the set of the Φ(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f’s such that their prime divisors are all equal to ±1 modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c 2 {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.
Abstract
Given c, a positive integer, we set M(f, c) := 2/Φ(f) ∑ χ∈X− f χ(c)|L(1, χ)|2, where X− f is the set of the Φ(f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f’s such that their prime divisors are all equal to ±1 modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c 2 {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.
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