A SURVEY OF RAMANUJAN EXPANSIONS

DOI10.1142/S1793042110003800zbMath1222.11003MaRDI QIDQ3074572

Lutz G. Lucht

Publication date: 9 February 2011

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

Dirichlet seriesEuler productsRamanujan expansionsarithmetic functions

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items

Arithmetic Functions: A Pivotal Topic in the Scientific Work of Wolfgang Schwarz ⋮ Remembering Wolfgang Schwarz, His Life and Work ⋮ On Ramanujan sums of a real variable and a new Ramanujan expansion for the divisor function ⋮ Invertibility of circulant matrices of arbitrary size ⋮ Ramanujan expansions of arithmetic functions of several variables ⋮ Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions ⋮ On the polynomial Ramanujan sums over finite fields ⋮ Obituary for Wolfgang Schwarz ⋮ On a Ramanujan type expansion of arithmetical functions ⋮ Certain weighted averages of generalized Ramanujan sums ⋮ On the Hardy-Littlewood prime tuples conjecture and higher convolutions of Ramanujan sums ⋮ ON AN EXTENSION OF LUCHT’S THEOREM ⋮ Sums of products of Ramanujan sums ⋮ On Ramanujan expansions with multiplicative coefficients ⋮ Ramanujan sums as supercharacters ⋮ Weighted inversion of general Dirichlet series ⋮ Power series with the von Mangoldt function ⋮ Ramanujan-Fourier series and a theorem of Ingham ⋮ On the error term in a Parseval type formula in the theory of Ramanujan expansions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A mean-value theorem for multiplicative functions
• Ramanujan expansions of bounded arithmetic functions
• Charakterisierung der additiven, fast-geraden Funktionen
• Some remarks on almost-even and almost-periodic functions
• Fourier analysis of arithmetical functions
• An application of Banach algebra techniques to multiplicative functions
• Ramanujan expansions revisited
• Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen
• Das asymptotische Verhalten von Summen über multiplikative Funktionen. II
• Sur les fonctions arithmétiques multiplicatives
• Almost Periodicity and the Representation of Integers as Sums of Squares