Preview

Chebyshevskii Sbornik

Advanced search

MOSCOW TALK: THE THEOREM ON APPROXIMATION OF TRIGONOMETRIC SUM BY A SHORT ONE (ATS)

https://doi.org/10.22405/2226-8383-2015-16-1-6-18

Abstract

The invited talk presented at the seminar of Prof. B. S. Kashin and Prof. S. V. Konyagin at the Faculty of Mechanics and Mathematics of Moscow Lomonosow University at the November 9, 2006.

 

About the Author

A. A. Karatsuba
Moscow State Universitynamed after M. V. Lomonosov
Russian Federation

Doctor of Physical and Mathematical Sciences, Professor, Head of Department of Number Theory Mathematics Institute. Russian Academy of Sciences, professor of the Moscow State University named after M. V. Lomonosov



References

1. Karatsuba, A. A., 1987, "Approximation of exponential sums by shorter ones." , Proc. Indian. Acad. Sci. (Math. Sci.), Vol. 97 (1–3), pp. 167–178.

2. Voronin, S. M. & Karatsuba, A. A., 1994, "The Riemann zeta-function" , Moscow: Phys.-Math. Lit., 376 p. (Russian).

3. Voronoi, G., 1903, "Sur un probl´eme du calcul des fonctions asymptotiques." , Journal f¨ur die reine und angewandte Mathematik 126, s. 241–282.

4. Hardy, G. H. & Littlewood, J. E., 1914, "The trigonometrical series associated with the elliptic θ -functions" , Acta Math. 37, pp. 193–239.

5. Vinogradov, I. M., 1917, "On the average value of the number of classes of purely root form of the negative determinant" , Communications of Kharkhov Mathematics Society 16, pp. 10–38.

6. Van der Corput, J. G., 1922, "Versch¨arfung der absch¨atzung beim teilerproblem" , Math. Ann., 87, pp. 39–65.

7. Vinogradov, I. M., 1976, "Special Variants of the Method of Trigonometric Sums" , Moscow: Nauka, pp. 1–122.

8. Karatsuba, A. A., 1981, "On the distance between adjacent zeros of the Riemann zeta function lying on the critical line." , Proc. Steklov Inst. Math., 157, pp. 51– 66 (1983); translation from Trudy Mat. Inst. Steklova, 157, pp. 49–63.

9. Moser J., On a certain sum in the theory of the Riemann zeta-function, Acta Arith. 31 (1976), pp. 34–43; Correction to the paper: Acta Arith., 31 (1976), pp. 31–43, pp. 45–51 (1976), Acta Arith. 35, pp. 403–404 (1979), Acta Arith. 40, pp. 97–107 (1981).

10. Ivic, A., 1983, "Topics in Recent Zeta- Function Theory" , Publ. Math. d’Orsay, Uni- versite de Paris-Sud, Orsay, pp. 1–272.

11. Narozhny, N. B.& Sanchez-Mondragon, J. J.& and Eberly, J. H., 1981, "Coherence versus incoherence: collapse and revival in a single quantum model," Phys. Rev. A, 23, pp. 236–247.

12. Fleischhauer, M. & Schleich, W. P., 1993, "Revivals made simple: Poisson summation formula as a key to the revivals in the Jaynes-Cummings model." , Phys. Rev. A, 47:3, pp. 4258–4269.

13. Chassande-Mottin E. & Pai A., 2006 "Best chirplet chain: Near-optimal detection of gravitational wave chirps" , Phys. Rev. D73, pp. 042003, 1 – 23.

14. Karatsuba E. A., 2004, "Approximation of sums of oscillating summands in certain physical problems" , Journal of Mathem. physics, Vol.45, 11, pp. 4310– 4321.

15. Карацуба E. A., 2005, "Approximation of exponential sums in the problem on the oscillator motion caused by pushes." Chebyshevskii Sb., Vol. 6, 3(15), pp. 205–224.


Review

For citations:


Karatsuba A.A. MOSCOW TALK: THE THEOREM ON APPROXIMATION OF TRIGONOMETRIC SUM BY A SHORT ONE (ATS). Chebyshevskii Sbornik. 2015;16(1):6-18. (In Russ.) https://doi.org/10.22405/2226-8383-2015-16-1-6-18

Views: 508


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2226-8383 (Print)