Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MZM_2019_105_3_a11, author = {I. D. Shkredov}, title = {A {Short} {Remark} on the {Multiplicative} {Energy} of the {Spectrum}}, journal = {Matemati\v{c}eskie zametki}, pages = {444--454}, publisher = {mathdoc}, volume = {105}, number = {3}, year = {2019}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a11/} }
I. D. Shkredov. A Short Remark on the Multiplicative Energy of the Spectrum. Matematičeskie zametki, Tome 105 (2019) no. 3, pp. 444-454. http://geodesic.mathdoc.fr/item/MZM_2019_105_3_a11/
[1] T. Tao, V. Vu, Additive Combinatorics, Cambridge Univ. Press, Cambridge, 2006 | MR | Zbl
[2] T. F. Bloom, “A quantitative improvement for Roth's theorem on arithmetic progressions”, J. Lond. Math. Soc. (2), 93:3 (2016), 643–663 | DOI | MR | Zbl
[3] M.-C. Chang, “A polynomial bound in Freiman's theorem”, Duke Math. J., 113:3 (2002), 399–419 | DOI | MR | Zbl
[4] B. Green, “Some constructions in the inverse spectral theory of cyclic groups”, Combin. Probab. Comput., 12:2 (2003), 127–138 | MR | Zbl
[5] B. Green, “Spectral structure of sets of integers”, Fourier Analysis and Convexity, Birkhäuser Boston, Boston, MA, 2004, 83–96 | MR | Zbl
[6] T. Sanders, “On certain other sets of integers”, J. Anal. Math., 116:1 (2012), 53–82 | DOI | MR | Zbl
[7] T. Sanders, “On Roth's theorem on progressions”, Ann. of Math. (2), 174:1 (2011), 619–636 | DOI | MR | Zbl
[8] I. D. Shkredov, “O mnozhestvakh bolshikh trigonometricheskikh summ”, Izv. RAN. Ser. matem., 72:1 (2008), 161–182 | DOI | MR | Zbl
[9] I. D. Shkredov, “On sumsets of dissociated sets”, Online J. Anal. Comb., 4 (2009), 1–26 | MR
[10] I. D. Shkredov, “Prilozheniya teorii summ proizvedenii k mnozhestvam, izbegayuschim neskolko lineinykh uravnenii”, Matem. sb., 209:4 (2018), 117–142 | DOI | Zbl
[11] M. Rudnev, “On the number of incidences between planes and points in three dimensions”, Combinatorica, 38:1 (2018), 219–254 | DOI | MR | Zbl
[12] M. Rudnev, I. D. Shkredov, S. Stevens, On the Energy Variant of the Sum-Product Conjecture, 2016, arXiv: math.CO/1607.05053v2
[13] I. D. Shkredov, “On asymptotic formulae in some sum–product questions”, Mosc. J. Comb. Number Theory, 8:1 (2019), 15–41, arXiv: math.CO/1802.09066v2 | MR
[14] P. Thang, M. Tait, C. Timmons, “A Szemerédi–Trotter type theorem, sum-product estimates in finite quasifields, and related results”, J. Combin. Theory Ser. A, 147 (2017), 55–74 | DOI | MR | Zbl
[15] L. A. Vinh, “A Szemerédi–Trotter type theorem and sum-product estimate over finite fields”, European J. Combin., 32:8 (2011), 1177–1181 | DOI | MR | Zbl
[16] B. Murphy, G. Petridis, Ol. Roche–Newton, M. Rudnev, I. D. Shkredov, New Results on Sum-Product Type Growth Over Fields, 2017, arXiv: math.CO/1702.01003v2
[17] S. Stevens, F. de Zeeuw, “An improved point-line incidence bound over arbitrary fields”, Bull. Lond. Math. Soc., 49:5 (2017), 842–858 | MR | Zbl
[18] G. Petridis, Products of Differences in Prime Order Finite Fields, 2016, arXiv: math.CO/1602.02142
[19] S. V. Konyagin, I. Shparlinski, Character Sums with Exponential Functions and Their Applications, Cambridge Univ. Press, Cambridge, 1999 | MR | Zbl
[20] E. Aksoy Yazici, B. Murphy, M. Rudnev, I. Shkredov, “Growth estimates in positive characteristic via collisions”, Int. Math. Res. Not. IMRN, 2017:23 (2017), 7148–7189 | DOI | MR | Zbl