RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Chebyshevskii Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Chebyshevskii Sb., 2015, Volume 16, Issue 1, Pages 176–190 (Mi cheb374)  

This article is cited in 6 scientific papers (total in 7 papers)

INTERNATIONAL CONFERENCE IN MEMORY OF A. A. KARATSUBA ON NUMBER THEORY AND APPLICATIONS

About the modern problems of the theory of hyperbolic zeta-functions of lattices

N. M. Dobrovol'skii

Tula State Pedagogical University

Abstract: The article gives an expanded version of the report, the author of Made in January 30, 2015 in Moscow at an international conference, dedicated to the memory of Professor A. A. Karatsuba, held at the Mathematical Institute. Russian Academy of Sciences and Moscow State University named after M. V. Lomonosov.
The report sets out the facts from the history of the theory of hyperbolic zeta function, provides definitions and notation.
The main content of the report was focused discussion of actual problems of the theory of hyperbolic zeta function of lattices. Identified the following promising areas of current research:
  • The problem of the correct order of decreasing hyperbolic zeta function in $ \alpha \to \infty $;
  • The problem of existence of analytic continuation in the left half-plane $ \alpha = \sigma + it   (\sigma \le1) $ hyperbolic zeta function of lattices $ \zeta_H (\Lambda | \alpha) $;
  • Analytic continuation in the case of lattices S. M. Voronin $ \Lambda (F, q) $;
  • Analytic continuation in the case of joint lattice approximations;
  • Analytic continuation in the case of algebraic lattices   $ \Lambda (t, F) = t \Lambda (F) $;
  • Analytic continuation in the case of an arbitrary lattice $ \Lambda$;
  • The problem behavior hyperbolic zeta function of lattices   $ \zeta_H (\Lambda | \alpha) $ in the critical strip;
  • The problem of values of trigonometric sums grids.

As a promising method for investigating these problems has been allocated an approach based on the study of the possibility of passing to the limit by a convergent sequence of Cartesian grids.
Bibliography: 19 titles.

Keywords: lattice, hyperbolic zeta function of lattice, net, hyperbolic zeta function of net, quadrature formula, parallelepiped net, method of optimal coefficients.

Full text: PDF file (331 kB)
References: PDF file   HTML file
UDC: 511.3
Received: 31.01.2015

Citation: N. M. Dobrovol'skii, “About the modern problems of the theory of hyperbolic zeta-functions of lattices”, Chebyshevskii Sb., 16:1 (2015), 176–190

Citation in format AMSBIB
\Bibitem{Dob15}
\by N.~M.~Dobrovol'skii
\paper About the modern problems of the theory of hyperbolic zeta-functions of~lattices
\jour Chebyshevskii Sb.
\yr 2015
\vol 16
\issue 1
\pages 176--190
\mathnet{http://mi.mathnet.ru/cheb374}
\elib{http://elibrary.ru/item.asp?id=23384583}


Linking options:
  • http://mi.mathnet.ru/eng/cheb374
  • http://mi.mathnet.ru/eng/cheb/v16/i1/p176

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, V. N. Chubarikov, “O konferentsii pamyati Anatoliya Alekseevicha Karatsuby po teorii chisel i prilozheniyam”, Chebyshevskii sb., 16:1 (2015), 89–152  mathnet  mathscinet  elib
    2. N. M. Dobrovolskii, N. N. Dobrovolskii, “O minimalnykh mnogochlenakh ostatochnykh drobei dlya algebraicheskikh irratsionalnostei”, Chebyshevskii sb., 16:3 (2015), 147–182  mathnet  elib
    3. N. M. Dobrovol'skii, I. N. Balaba, I. Yu. Rebrova, N. N. Dobrovol'skii, “On Lagrange algorithm for reduced algebraic irrationalities”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2016, no. 2, 27–39  mathnet
    4. N. M. Dobrovolskii, N. N. Dobrovolskii, D. K. Sobolev, V. N. Soboleva, “Klassifikatsiya chisto-veschestvennykh algebraicheskikh irratsionalnostei”, Chebyshevskii sb., 18:2 (2017), 98–128  mathnet  crossref  elib
    5. S. S. Demidov, E. A. Morozova, V. N. Chubarikov, I. Yu. Rebrova, I. N. Balaba, N. N. Dobrovolskii, N. M. Dobrovolskii, L. P. Dobrovolskaya, A. V. Rodionov, O. A. Pikhtilkova, “Teoretiko-chislovoi metod v priblizhennom analize”, Chebyshevskii sb., 18:4 (2017), 6–85  mathnet  crossref  elib
    6. I. Yu. Rebrova, A. V. Kirilina, “N. M. Korobov i teoriya giperbolicheskoi dzeta-funktsii reshetok”, Chebyshevskii sb., 19:2 (2018), 341–367  mathnet  crossref  elib
    7. N. N. Dobrovolskii, “O dvukh asimptoticheskikh formulakh v teorii giperbolicheskoi dzeta-funktsii reshetok”, Chebyshevskii sb., 19:3 (2018), 109–134  mathnet  crossref  elib
  • Number of views:
    This page:162
    Full text:71
    References:31

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020