EXPONENTIAL AND CHARACTER SUMS WITH MERSENNE NUMBERS
نویسندگان
چکیده
منابع مشابه
Sums of Prime Divisors and Mersenne Numbers
The study of the function β(n) originated in the paper of Nelson, Penney, and Pomerance [7], where the question was raised as to whether the set of Ruth-Aaron numbers (i.e., natural numbers n for which β(n) = β(n+ 1)) has zero density in the set of all positive integers. This question was answered in the affirmative by Erdős and Pomerance [5], and the main result of [5] was later improved by Po...
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This is a collection of mostly unrelated open questions, at various levels of difficulty, related to exponential and multiplicative character sums. One may certainly notice a large proportion of self-references in the bibliography. By no means should this be considered as an indication of anything else than the fact that the choice of problems reflects the taste and interests of the author. Thu...
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We present an algorithm for computing the class number of the quadratic number field of discriminant d. The algorithm terminates unconditionally with the correct answer and, under the GRH, executes in Oε(|d|) steps. The technique used combines algebraic methods with Burgess’ theorem on character sums to estimate L(1, χd). We give an explicit version of Burgess’ theorem valid for prime discrimin...
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A catalogue record of this book is available from the British Library Library of Congress Cataloguing in Publication data Kon iagin, S. V. (Sergeˇı Vladimirovich) Character sums with exponential functions and their applications
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The first seventeen even perfect numbers are therefore obtained by substituting these values of ra in the expression 2n_1(2n —1). The first twelve of the Mersenne primes have been known since 1914; the twelfth, 2127 —1, was indeed found by Lucas as early as 1876, and for the next seventy-five years was the largest known prime. More details on the history of the Mersenne numbers may be found in ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2012
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788712000109