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Titlebook: Topics in Analytic Number Theory; Hans Rademacher Book 1973 Springer-Verlag, Berlin ? Heidelberg 1973 analytic number theory.binomial.numb

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書目名稱Topics in Analytic Number Theory
編輯Hans Rademacher
視頻videohttp://file.papertrans.cn/927/926076/926076.mp4
叢書名稱Grundlehren der mathematischen Wissenschaften
圖書封面Titlebook: Topics in Analytic Number Theory;  Hans Rademacher Book 1973 Springer-Verlag, Berlin ? Heidelberg 1973 analytic number theory.binomial.numb
描述At the time of Professor Rademacher‘s death early in 1969, there was available a complete manuscript of the present work. The editors had only to supply a few bibliographical references and to correct a few misprints and errors. No substantive changes were made in the manu- script except in one or two places where references to additional material appeared; since this material was not found in Rademacher‘s papers, these references were deleted. The editors are grateful to Springer-Verlag for their helpfulness and courtesy. Rademacher started work on the present volume no later than 1944; he was still working on it at the inception of his final illness. It represents the parts of analytic number theory that were of greatest interest to him. The editors, his students, offer this work as homage to the memory of a great man to whom they, in common with all number theorists, owe a deep and lasting debt. E. Grosswald Temple University, Philadelphia, PA 19122, U.S.A. J. Lehner University of Pittsburgh, Pittsburgh, PA 15213 and National Bureau of Standards, Washington, DC 20234, U.S.A. M. Newman National Bureau of Standards, Washington, DC 20234, U.S.A. Contents I. Analytic tools Chapter 1
出版日期Book 1973
關(guān)鍵詞analytic number theory; binomial; number theory
版次1
doihttps://doi.org/10.1007/978-3-642-80615-5
isbn_softcover978-3-642-80617-9
isbn_ebook978-3-642-80615-5Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag, Berlin ? Heidelberg 1973
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The Euler-MacLaurin Sum FormulaLet .(.) be continuous with as many continuous derivatives as required. Noticing .′.(.) =l we obtain through integration by parts
板凳
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The Eisenstein SeriesLet .,. be two complex numbers, different from zero, such that the quotient . =./. is not real. The totality . of all complex numbers . + . with . integers, forms a point-lattice in the complex plane.
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The Transformation of log η(τ) and the Theory of the Dedekind SumsThe direct determination of the . constant . = .(.) belongs to the theory of the ?-functions and Gaussian sums.
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The ?-functionsWhereas there exist doubly periodic . functions, as we have seen in § 57, entire doubly periodic functions can only be constants, since they are bounded in their fundamental parallelogram and thus in the whole plane.
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Application of the Circle Method to Modular Forms of Positive DimensionThe circle method, which led to an explicit formula for the Fourier coefficients . (.) of . .(.)., can be generalized to deal with general modular forms of positive dimension.
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https://doi.org/10.1007/978-3-642-80615-5analytic number theory; binomial; number theory
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978-3-642-80617-9Springer-Verlag, Berlin ? Heidelberg 1973
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