The sum-product theorem in \(\mathbb Z_q\) with \(q\) arbitrary

DOI10.1007/s11854-008-0044-2zbMath1214.11017OpenAlexW2045963062MaRDI QIDQ1001386

Jean Bourgain

Publication date: 17 February 2009

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11854-008-0044-2

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Additive bases, including sumsets (11B13)

Related Items (7)

Expansion and random walks in \(\text{SL}_d(\mathbb{Z}/p^n\mathbb{Z})\). II. ⋮ Arithmetic and dynamics on varieties of Markoff type ⋮ The sum-product estimate for large subsets of prime fields ⋮ Sum-product phenomena: \(\mathfrak{P}\)-adic case ⋮ On three-variable expanders over finite valuation rings ⋮ From Apollonius to Zaremba: Local-global phenomena in thin orbits ⋮ Differencing methods for Korobov-type exponential sums

Cites Work

• Unnamed Item
• Unnamed Item
• A sum-product estimate in finite fields, and applications
• Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).
• Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
• Exponential sum estimates over subgroups of \(\mathbb Z^*_q\), \(q\) arbitrary
• On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\)
• Exponential sum estimates over subgroups and almost subgroups of \(\mathbb Z_Q^*\), where \(Q\) is composite with few prime factors
• A Gauss sum estimate in arbitrary finite fields
• On the Erdős-Volkmann and Katz-Tao ring conjectures
• Sieving and expanders
• Estimates on exponential sums related to the Diffie-Hellman distributions
• New bounds for Gauss sums derived from KTH powers, and for Heilbronn's exponential sum
• Mordell’s exponential sum estimate revisited
• ESTIMATES FOR THE NUMBER OF SUMS AND PRODUCTS AND FOR EXPONENTIAL SUMS IN FIELDS OF PRIME ORDER
• Extracting Randomness Using Few Independent Sources
• Simulating independence
• Some connections between Falconer's distance set conjecture and sets of Furstenburg type

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