Distributions with automorphy and Dirichlet series
نویسندگان
چکیده
منابع مشابه
Distributions and Analytic Continuation of Dirichlet Series
Dirichlet series and Fourier series can both be used to encode sequences of complex numbers an , n ∈ N. Dirichlet series do so in a manner adapted to the multiplicative structure of N, whereas Fourier series reflect the additive structure of N. Formally at least, the Mellin transform relates these two ways of representing sequences. In this paper, we make sense of the Mellin transform of period...
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where the an are complex numbers and s is a complex variable. Such functions are called Dirichlet series. We call a1 the constant term. A Dirichlet series will often be written as ∑ ann −s, with the index of summation understood to start at n = 1. Similarly, ∑ app −s runs over the primes, and ∑ apkp −ks runs over the prime powers excluding 1. (Not counting 1 as a prime power in that notation is...
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Dedicated to Professor Y. S. Chow on the Occasion of his 80th Birthday By Robert W. Keener and Wei Biao Wu Abstract Let Y have a symmetric Dirichlet multinomial distributions in R, and let Sm = h(Y1)+· · ·+h(Ym). We derive a central limit theorem for Sm as the sample size n and the number of cells m tend to infinity at the same rate. The rate of convergence is shown to be of order m. The approa...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1979
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000018377