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TitleNumber Theory and Analysis [electronic resource] : A Collection of Papers in Honor of Edmund Landau (1877-1938) / edited by Paul Turรกn
ImprintBoston, MA : Springer US : Imprint: Springer, 1969
Connect tohttp://dx.doi.org/10.1007/978-1-4615-4819-5
Descript 356 p. 3 illus. online resource

SUMMARY

February 14, 1968 marked the thirtieth year since the death of Edmund Landau. The papers of this volume are dedicated by friends, students, and admirers to the memory of this outstanding scholar and teacher. To mention but one side of his original and varied scientific work, the results and effects of which cannot be disยญ cussed here, Edmund Landau performed one of his greatest services in developing the analytic theory of prime numbers from a subject accessible only with great difficulty even to the initiated few to the general estate of mathematicians. With the exception of the work of Chebyshev, Riemann, and Mertens, before Landau the problems of this theory were attempted only in a number of papers which were filled with gaps and errors. These problems were such that even Gauss abandoned them after several attempts in his youth, and they were described by N. H. Abel in a letter of 1823 and by O. Toeplitz in a lecture in 1930 as the deepest part of matheยญ matics. Clarification first began with the papers of Hadamard, de la Vallee Poussin, and von Mangoldt. At the end ofthe foreword to his work" Handbuch der Lehre von der Verteilung der Primzahlen" which appeared in 1909, Landau could thus remark with complete justification: " . . . The difficulty of the previously unsolved problems has frightened nearly everyone away from the theory of prime numbers


CONTENT

On the large sieve method -- ร{156}ber binรคre additive Probleme gemischter Art -- How to extend a Calculus -- On the representation of positive integers as sums of three cubes of positive rational numbers -- Analytische Klassenzahlformeln -- ร{156}ber Folgen ganzer Zahlen -- On the average length of a class of finite continued fractions -- Interpolation analytischer Funktionen auf dem Einheitskreis -- On the high-indices theorem for Borel summability -- Bemerkungen zu Landauschen Methoden in der Gitterpunktlehre -- ร{156}ber einige Fragen der vergleichenden Primzahltheorie -- On local theorems for additive number-theoretic functions -- The โ{128}{156}pits effectโ{128}{157} for the integral function -- On numbers which can be expressed as a sum of powers -- On some Diophantine equations y2 = x3 + k with no rational solutions (II) -- ร{156}ber das Vorzeichen des Restgliedes im Primzahlsatz -- A measure for the differential-transcendence of the zeta-function of Riemann -- Comments on Eulerโ{128}{153}s โ{128}{156}De mirabilibus proprietatibus numerorum pentagonaliumโ{128}{157} -- On the distribution of numbers prime to n -- Spline interpolation and the higher derivatives -- Zu den Beweisen des Vorbereitungssatzes von Weierstraร{159} -- ร{156}ber Gitterpunkte in mehrdimensionalen Kugeln IV -- Publications of Edmund Landau


Mathematics Number theory Mathematics Number Theory



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