Titlebook: Number Theory and Modular Forms; Papers in Memory of Bruce Berndt,Ken Ono Book 2003 Springer-Verlag US 2003 Lattice.Prime.continued fracti

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,Modular Transformations of Ramanujan’s Fifth and Seventh Order Mock Theta Functions,and seventh order mock theta functions under the modular group generators τ → τ + 1 and τ → −1/τ, where . = ... The transformation formulas are more complex than those of ordinary theta functions. A definition of the order of a mock theta function is also given.

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On Dirichlet Series for Sums of Squares,cations of Theorem 2.1 is to obtain closed forms, in terms of . (.) and Dirichlet .-functions, for the generating functions of ..(.), ..(.), .. (.) and .. (.). for certain . and .. We also use these generating functions to obtain asymptotic estimates of the average values for each function for which we obtain a Dirichlet series.

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Book 2003 at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin‘s life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin‘

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Developments in Mathematicshttp://image.papertrans.cn/n/image/668875.jpg