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Diophantine ApproximationDiophantine EquationFinite FieldsFourier CoefficientsDirichlet SeriesReal Quadratic FieldsEisenstein SeriesAlgebraic IndependenceS TheoremAsymptotic FormulaHausdorff DimensionArithmeticRiemann Zeta FunctionMahler MeasureLinear Forms in LogarithmsArithmetic ProgressionCircle MethodQuadratic Number FieldsRiemann HypothesisBinomial Coefficients