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Mat. Zametki, 2000, Volume 68, Issue 6, Pages 842–850 (Mi mz1006)  

This article is cited in 14 scientific papers (total in 14 papers)

On Lower Bounds for the $L_1$-Norm of Exponential Sums

M. Z. Garaev

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Abstract: In the paper a method for finding lower bounds of the $L_1$-norm of some exponential sums is described.

DOI: https://doi.org/10.4213/mzm1006

Full text: PDF file (172 kB)
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English version:
Mathematical Notes, 2000, 68:6, 713–720

Bibliographic databases:

UDC: 511.3
Received: 01.06.2000

Citation: M. Z. Garaev, “On Lower Bounds for the $L_1$-Norm of Exponential Sums”, Mat. Zametki, 68:6 (2000), 842–850; Math. Notes, 68:6 (2000), 713–720

Citation in format AMSBIB
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\by M.~Z.~Garaev
\paper On Lower Bounds for the $L_1$-Norm of Exponential Sums
\jour Mat. Zametki
\yr 2000
\vol 68
\issue 6
\pages 842--850
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\crossref{https://doi.org/10.4213/mzm1006}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1835182}
\zmath{https://zbmath.org/?q=an:1005.11037}
\transl
\jour Math. Notes
\yr 2000
\vol 68
\issue 6
\pages 713--720
\crossref{https://doi.org/10.1023/A:1026600414468}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000166684000022}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Garaev, MZ, “L-1-norms of exponential sums and the corresponding additive problem”, Zeitschrift fur Analysis und Ihre Anwendungen, 20:4 (2001), 999  crossref  mathscinet  zmath  isi
    2. Garaev, MZ, “On the Waring-Goldbach problem with small non-integer exponent”, Acta Arithmetica, 108:3 (2003), 297  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Garaev, MZ, “On cardinality of sumsets”, Journal of the Australian Mathematical Society, 78 (2005), 221  crossref  mathscinet  zmath  isi
    4. Garaev, MZ, “Upper bounds for the number of solutions of a diophantine equation”, Transactions of the American Mathematical Society, 357:6 (2005), 2527  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Iosevich, A, “Combinatorial complexity of convex sequences”, Discrete & Computational Geometry, 35:1 (2006), 143  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Garaev, MZ, “On an additive representation associated with the L-1-norm of an exponential sum”, Rocky Mountain Journal of Mathematics, 37:5 (2007), 1551  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Garaev, MZ, “On the number of solutions of a diophantine equation with symmetric entries”, Journal of Number Theory, 125:1 (2007), 201  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Schoen T., Shkredov I.D., “On Sumsets of Convex Sets”, Comb. Probab. Comput., 20:5 (2011), 793–798  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Schoen T., “On Convolutions of Convex Sets and Related Problems”, Can. Math. Bul.-Bul. Can. Math., 57:4 (2014), 877–883  crossref  mathscinet  zmath  isi  scopus  scopus
    10. I. D. Shkredov, “On sums of Szemerédi–Trotter sets”, Proc. Steklov Inst. Math., 289 (2015), 300–309  mathnet  crossref  crossref  isi  elib
    11. Raz O.E., Sharir M., Shkredov I.D., “On the number of unit-area triangles spanned by convex grids in the plane”, Comput. Geom.-Theory Appl., 62 (2017), 25–33  crossref  mathscinet  zmath  isi  scopus
    12. Aistleitner Ch., Larcher G., Lewko M., “Additive Energy and the Hausdorff Dimension of the Exceptional Set in Metric Pair Correlation Problems”, Isr. J. Math., 222:1 (2017), 463–485  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Li J., Shakan G., “On Distinct Consecutive R-Differences”, J. Number Theory, 199 (2019), 363–376  crossref  mathscinet  zmath  isi  scopus
    14. K. I. Olmezov, “Sharpening an Estimate of the Size of the Sumset of a Convex Set”, Math. Notes, 107:6 (2020), 954–957  mathnet  crossref  crossref  isi  elib
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