An extension of Ramanujan's sum
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Publication:2648020
DOI10.1215/S0012-7094-49-01607-5zbMath0034.02105MaRDI QIDQ2648020
Publication date: 1949
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Arithmetic functions; related numbers; inversion formulas (11A25) Arithmetic theory of polynomial rings over finite fields (11T55)
Related Items (25)
Arithmetic Functions of Polynomials ⋮ Some properties of the extended Ramanujan sums ⋮ On the polynomial Ramanujan sums over finite fields ⋮ On a Ramanujan type expansion of arithmetical functions ⋮ Explicit transformations for generalized Lambert series associated with the divisor function \(\sigma_a^{(N)}(n)\) and their applications ⋮ Sums of weighted averages of gcd-sum functions. II ⋮ Unnamed Item ⋮ Certain weighted averages of generalized Ramanujan sums ⋮ On the distribution of Ramanujan sums over number fields ⋮ On Ramanujan sums over a Dedekind domain with finite norm property ⋮ Unnamed Item ⋮ A New Generalization of Three Identities of Ramanujan and Suryanarayana ⋮ Moments of averages of generalized Ramanujan sums ⋮ On an Identity of Eckford Cohen ⋮ Ramanujan sums as supercharacters ⋮ An elementary estimate for the $k$-free integers ⋮ On a generalization of the Dedekind-Hölder theorem ⋮ The number of restricted solutions of some systems of linear congruences ⋮ Generalized Ramanujan's sum ⋮ Sums of weighted averages of gcd-sum functions ⋮ The Ramanujan sum and Chebotarev densities ⋮ Ramanujan’s sum in the ring of integers of an algebraic number field ⋮ On a congruence equation and related arithmetical identities ⋮ Über die Zahl der in einem \(k\)-reduzierten Restsystem liegenden Lösungen einer Kongruenz \(x_ 1 +x_ 2 +\cdots +x_ r\equiv a(m^ k)\) ⋮ The discrete Fourier transform of \((r, s)\)-even functions
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