منابع مشابه
Transformations of Fourier Coefficients
Introduction. In 1923 M. Fekete [2]2 introduced the concept of factor sequences that left invariant the class of a Fourier series. That is, Fekete investigated the conditions to which a sequence of constants (X„) must be subjected in order that (X„a„, X„i„) be Fourier coefficients of a function of the same class, K, as that of the function determined by (an, bn). Whenever (X„) has this property...
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The Möbius inversion technique is applied to the Poisson summation formula. This results in expressions for the remainder term in the Fourier coefficient asymptotic expansion as an infinite series. Each element of this series is a remainder term in the corresponding Euler-Maclaurin summation formula, and the series has specified convergence properties. These expressions may be used as the basis...
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We provide systematic evaluations, in terms of binary quadratic representations of 4p, for the p-th Fourier coefficients of each member f of an infinite class C of CM eigenforms. As an application, previously conjectured evaluations of three algebro-geometric character sums can now be formulated explicitly without reference to eigenforms. There are several non-CM newforms that appear to share s...
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These notes describe some conjectures and results related to the distribution of Fourier coefficients of modular forms. This is a rough draft and these notes should forever be considered incomplete.
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1. INTRODUCTION. Edge detection and the detection of discontinuities are important in many fields. In image processing, for example, one often needs to determine the boundaries of the items of which a picture is composed. (For more information about edge detection in image processing, see [10].) We consider the problem of detecting the edges present in a function when given the Fourier coeffici...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1952
ISSN: 0002-9939
DOI: 10.2307/2032181