About: Rudin's conjecture

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Rudin's conjecture is a mathematical hypothesis (in additive combinatorics and elementary number theory) concerning an upper bound for the number of squares in finite arithmetic progressions. The conjecture, which has applications in the theory of trigonometric series, was first stated by Walter Rudin in his 1960 paper Trigonometric series with gaps.

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  • Rudin's conjecture is a mathematical hypothesis (in additive combinatorics and elementary number theory) concerning an upper bound for the number of squares in finite arithmetic progressions. The conjecture, which has applications in the theory of trigonometric series, was first stated by Walter Rudin in his 1960 paper Trigonometric series with gaps. For positive integers define the expression to be the number of perfect squares in the arithmetic progression , for , and define to be the maximum of the set {Q(N; q, a) : q, a ≥ 1} . Rudin's conjecture asserts (in big O notation) that and in its stronger form that, if , . (en)
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  • Rudin's conjecture is a mathematical hypothesis (in additive combinatorics and elementary number theory) concerning an upper bound for the number of squares in finite arithmetic progressions. The conjecture, which has applications in the theory of trigonometric series, was first stated by Walter Rudin in his 1960 paper Trigonometric series with gaps. (en)
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  • Rudin's conjecture (en)
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