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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 1997, Volume 218, Pages 179–189 (Mi tm958)  
This article is cited in 7 scientific papers (total in 8 papers)

On the convergence exponent of trigonometric integrals

I. A. Ikromov

International Centre for Theoretical Physics, Trieste, Italy
Full-text PDF (962 kB) Citations (8)
Abstract: The method of trigonometric sums is one of the most powerful tools in analytic number theory. In particular trigonometric integrals play an important role. Moreover, many problems in both mathematical physics and theory of probability lead to investigation of trigonometric integrals. Namely, it is important asymptotic behavior, estimation and summation exponent with respect to parameters of such integrals.
In this paper we consider multi-dimensional trigonometric integrals with polynomial phases and get a lower estimation for convergence exponent of functions defined by such integrals. Moreover, we obtain explicit value of convergence exponent in particular cases.
Received in February 1997
Bibliographic databases:
UDC: 511
Language: English
Citation: I. A. Ikromov, “On the convergence exponent of trigonometric integrals”, Analytic number theory and applications, Collection of papers. To Prof. Anatolii Alexeevich Karatsuba on occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 218, Nauka, Moscow, 1997, 179–189; Proc. Steklov Inst. Math., 218 (1997), 175–185
Citation in format AMSBIB
\Bibitem{Ikr97}
\by I.~A.~Ikromov
\paper On the convergence exponent of trigonometric integrals
\inbook Analytic number theory and applications
\bookinfo Collection of papers. To Prof. Anatolii Alexeevich Karatsuba on occasion of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 1997
\vol 218
\pages 179--189
\publ Nauka
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm958}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1636721}
\zmath{https://zbmath.org/?q=an:0909.11032}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1997
\vol 218
\pages 175--185
Linking options:
  • https://www.mathnet.ru/eng/tm958
  • https://www.mathnet.ru/eng/tm/v218/p179
    Addendum
    This publication is cited in the following 8 articles:
    1. I. A. Ikromov, “Letter to the Editor: Addition to the Paper “On the Convergence Exponent of Trigonometric Integrals””, Proc. Steklov Inst. Math., 319 (2022), 307–310  mathnet  crossref  crossref  mathscinet
    2. M. A. Chahkiev, “Exact value of the exponent of convergence of the singular integral in Tarry's problem for homogeneous polynomials of degree n in two variables”, Izv. Math., 85:2 (2021), 332–340  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    3. I. Sh. Jabbarov, “Convergence Exponent of a Special Integral in the Two-Dimensional Tarry Problem with Homogeneous Polynomial of Degree 2”, Math. Notes, 105:3 (2019), 359–365  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Safarov A.R., “On the l-P-Bound For Trigonometric Integrals”, Anal. Math., 45:1 (2019), 153–176  crossref  mathscinet  zmath  isi  scopus
    5. I. A. Ikromov, “Summability of Oscillatory Integrals over Parameters and the Boundedness Problem for Fourier Transforms on Curves”, Math. Notes, 87:5 (2010), 700–719  mathnet  crossref  crossref  mathscinet  isi  elib
    6. M. A. Chahkiev, “Estimates for oscillatory integrals with convex phase”, Izv. Math., 70:1 (2006), 171–209  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. M. A. Chahkiev, “On the convergence exponent of the singular integral in the multi-dimensional analogue of Tarry's problem”, Izv. Math., 67:2 (2003), 405–418  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Chakhkiev M.A., “The exponent of convergence of the singular integral in a multidimensional analog of the Terry problem”, Doklady Mathematics, 67:3 (2003), 320–322  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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