Ramanujan–Fourier series, the Wiener–Khintchine formula and the distribution of prime pairs

نویسندگان

  • H. Gopalkrishna Gadiyar
  • R. Padma
چکیده

The Wiener–Khintchine formula plays a central role in statistical mechanics. It is shown here that the problem of prime pairs is related to autocorrelation and hence to a Wiener–Khintchine formula. “Experimental” evidence is given for this. c © 1999 Elsevier Science B.V. All rights reserved. PACS: 05.40+j; 02.30.Nw; 02.10.Lh

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Rota meets Ramanujan: Probabilistic interpretation of Ramanujan - Fourier series

In this paper the ideas of Rota and Ramanujan are shown to be central to understanding problems in additive number theory. The circle and sieve methods are two different facets of the same theme of interplay between probability and Fourier series used to great advantage by Wiener in engineering. Norbert Wiener forged a powerful tool for electrical engineers by combining two distinct branches of...

متن کامل

Convolution and Cross-correlation of Ramanujan-fourier Series

where x̄ is the complex conjugate of x This paper uses the machinery of almost periodic functions to prove that even without uniform convergence the connection between a pair of almost periodic functions and the constants of the associated Fourier series exists for both the convolution and cross-correlation. The general results for two almost periodic functions are narrowed and applied to Ramanu...

متن کامل

Recursive Wiener-Khintchine Theorem

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (WienerKhintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this probl...

متن کامل

Some implications of Chu ’ s 10 ψ 10 extension of Bailey ’ s 6 ψ 6 summation formula

Lucy Slater used Bailey’s 6ψ6 summation formula to derive the Bailey pairs she used to construct her famous list of 130 identities of the Rogers-Ramanujan type. In the present paper we apply the same techniques to Chu’s 10ψ10 generalization of Bailey’s formula to produce quite general Bailey pairs. Slater’s Bailey pairs are then recovered as special limiting cases of these more general pairs. I...

متن کامل

Nonharmonic Gabor Expansions

We consider Gabor systems generated by a Gaussian function and prove certain classical results of Paley and Wiener on nonharmonic Fourier series of complex exponentials for the Gabor expansion‎. ‎In particular, we prove a version of Plancherel-Po ́lya theorem for entire functions with finite order of growth and use the Hadamard factorization theorem to study regularity‎, ‎exactness and deficienc...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999