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EFFECTIVE l 2 DECOUPLING FOR THE PARABOLA
Author(s) -
Li Zane Kun
Publication year - 2020
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12038
Subject(s) - mathematics , decoupling (probability) , conjecture , parabola , integer (computer science) , order (exchange) , elliptic curve , combinatorics , upper and lower bounds , mathematical analysis , pure mathematics , geometry , finance , control engineering , computer science , engineering , economics , programming language
We make effectivel 2 L pdecoupling for the parabola in the range 4 < p < 6 . In an appendix joint with Jean Bourgain, we apply the main theorem to prove the conjectural bound for the sixth‐order correlation of the integer solutions of the equationx 2 + y 2 = m in an extremal case. This proves unconditionally a result that was proven in Bombieri and Bourgain [ Int. Math. Res. Not. IMRN 2015 (11), 3343–3407] under the hypotheses of the Birch and Swinnerton–Dyer conjecture and the Riemann Hypothesis for L ‐functions of elliptic curves over Q .