Fourier series with positive coefficients
نویسندگان
چکیده
منابع مشابه
Power-monotone Sequences and Fourier Series with Positive Coefficients
J. Németh has extended several basic theorems of R. P. Boas Jr. pertaining to Fourier series with positive coefficients from Lipschitz classes to generalized Lipschitz classes. The goal of the present work is to find the common root of known results of this type and to establish two theorems that are generalizations of Németh’s results. Our results can be considered as sample examples showing t...
متن کاملOn Fourier Coefficients of Eisenstein Series
In this paper we wish to prove that under certain conditions the Fourier coefficients of the Eisenstein series for an arithmetic group acting on a tube domain are all rational numbers. Let G be a connected, simply-connected, semisimple, and almost Q-simple linear algebraic group defined over the rational number field Q. Let R be the real number field. Then GR is connected, and we assume that if...
متن کاملFourier coefficients of sextic theta series
This article focuses on the theta series on the 6-fold cover of GL2. We investigate the Fourier coefficients τ(r) of the theta series, and give partially proven, partially conjectured values for τ(π)2, τ(π2) and τ(π4) for prime values π.
متن کاملA Property of Power Series with Positive Coefficients
The following theorem is suggested by a problem in the theory of probability .' Let pk be a sequence of non-negative numbers for which Eó pk =1, and let m = Ei kpk <_ "0. Suppose further that P(x) _ E p kx k 0 is not a power series in xl for any integer t > 1. Then 1-P(x) has no zeros in the circle I x I < 1, and the series U(x) _ u • k x k 1-P(x) 0 has the property lim u n = 1/m. n-(If m= oo, ...
متن کاملComputer Algebra and Power Series with Positive Coefficients
We consider the question whether all the coefficients in the series expansions of some specific rational functions are positive, and we demonstrate how computer algebra can help answering questions arising in this context. By giving partial computer proofs, we provide new evidence in support of some longstanding open conjectures. Also two new conjectures are made.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1987
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1987-0902561-6