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

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Matematicheskie Zametki, 2000, Volume 68, Issue 6, Pages 842–850
DOI: https://doi.org/10.4213/mzm1006 (Mi mzm1006)

This article is cited in 19 scientific papers (total in 19 papers)

On Lower Bounds for the

L_{1}

$L_1$ -Norm of Exponential Sums

M. Z. Garaev

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Full-text PDF (172 kB) Citations (19)

References:

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

Abstract: In the paper a method for finding lower bounds of the

L_{1}

$L_1$ -norm of some exponential sums is described.

Received: 01.06.2000

English version:
Mathematical Notes, 2000, Volume 68, Issue 6, Pages 713–720
DOI: https://doi.org/10.1023/A:1026600414468

Bibliographic databases:

UDC: 511.3

Language: Russian

Citation: M. Z. Garaev, “On Lower Bounds for the

L_{1}

$L_1$ -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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\jour Math. Notes

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\vol 68

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\pages 713--720

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Linking options:

https://www.mathnet.ru/eng/mzm1006

https://doi.org/10.4213/mzm1006

https://www.mathnet.ru/eng/mzm/v68/i6/p842

This publication is cited in the following 19 articles:

Hanson B., Roche-Newton O., Rudnev M., “Higher Convexity and Iterated Sum Sets”, Combinatorica, 42:1 (2022), 71–85
Garaev M.Z., Garcia V.C., “On the Number of Representations By N! Modulo a Prime and Applications”, Mon.heft. Math., 198:3 (2022), 535–545
O. Roche-Newton, A. Warren, “A convex set with a rich difference”, Acta Math. Hungar., 168:2 (2022), 587
Imre Ruzsa, George Shakan, József Solymosi, Endre Szemerédi, Springer Proceedings in Mathematics & Statistics, 347, Combinatorial and Additive Number Theory IV, 2021, 425
K. I. Olmezov, “Sharpening an Estimate of the Size of the Sumset of a Convex Set”, Math. Notes, 107:6 (2020), 984–987
K. I. Olmezov, “Additive Properties of Slowly Increasing Convex Sets”, Math. Notes, 108:6 (2020), 827–841
Li J., Shakan G., “On Distinct Consecutive R-Differences”, J. Number Theory, 199 (2019), 363–376
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
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
I. D. Shkredov, “On sums of Szemerédi–Trotter sets”, Proc. Steklov Inst. Math., 289 (2015), 300–309
Schoen T., “On Convolutions of Convex Sets and Related Problems”, Can. Math. Bul.-Bul. Can. Math., 57:4 (2014), 877–883
Schoen T., Shkredov I.D., “On Sumsets of Convex Sets”, Comb. Probab. Comput., 20:5 (2011), 793–798
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
Garaev, MZ, “On the number of solutions of a diophantine equation with symmetric entries”, Journal of Number Theory, 125:1 (2007), 201
Iosevich, A, “Combinatorial complexity of convex sequences”, Discrete & Computational Geometry, 35:1 (2006), 143
Garaev, MZ, “On cardinality of sumsets”, Journal of the Australian Mathematical Society, 78 (2005), 221
Garaev, MZ, “Upper bounds for the number of solutions of a diophantine equation”, Transactions of the American Mathematical Society, 357:6 (2005), 2527
Garaev, MZ, “On the Waring-Goldbach problem with small non-integer exponent”, Acta Arithmetica, 108:3 (2003), 297
Garaev, MZ, “L-1-norms of exponential sums and the corresponding additive problem”, Zeitschrift fur Analysis und Ihre Anwendungen, 20:4 (2001), 999

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

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