pnt-declarations/PrimeNumberTheoremAnd.Mathlib.NumberTheory.ArithmeticFunction.jsonl

{"name":"ArithmeticFunction.sum_Icc_mul_zeta","declaration":"theorem ArithmeticFunction.sum_Icc_mul_zeta {R : Type u_1} [Semiring R] (f : ArithmeticFunction R) (N : ℕ) : (Finset.sum (Finset.Icc 1 N) fun d => (f * ↑ArithmeticFunction.zeta) d) =\n  Finset.sum (Finset.Icc 1 N) fun d => (N / d) • f d"}
{"name":"ArithmeticFunction.sum_range_mul_zeta","declaration":"theorem ArithmeticFunction.sum_range_mul_zeta {R : Type u_1} [Semiring R] (f : ArithmeticFunction R) (N : ℕ) : (Finset.sum (Finset.range (N + 1)) fun d => (f * ↑ArithmeticFunction.zeta) d) =\n  Finset.sum (Finset.range (N + 1)) fun d => (N / d) • f d"}