Diagonal cubic equations. II
نویسندگان
چکیده
منابع مشابه
Rational Solutions of Pairs of Diagonal Equations, One Cubic and One Quadratic
We obtain an essentially optimal estimate for the moment of order 32/3 of the exponential sum having argument αx + βx. Subject to modest local solubility hypotheses, we thereby establish that pairs of diagonal Diophantine equations, one cubic and one quadratic, possess nontrivial integral solutions whenever the number of variables exceeds 10.
متن کاملThe density of integral solutions for pairs of diagonal cubic equations
We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least thirteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least seven, we obtain a lower bound for the order of magnitude of the number of integral solutions con...
متن کاملQuasilinear Schrödinger Equations Ii: Small Data and Cubic Nonlinearities
In part I of this project we examined low regularity local well-posedness for generic quasilinear Schrödinger equations with small data. This improved, in the small data regime, the preceding results of Kenig, Ponce, and Vega as well as Kenig, Ponce, Rolvung, and Vega. In the setting of quadratic interactions, the (translation invariant) function spaces which were utilized incorporated an l sum...
متن کاملApproximately cubic functional equations and cubic multipliers
* Correspondence: abasalt. [email protected] Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran Full list of author information is available at the end of the article Abstract In this paper, we prove the Hyers-Ulam stability and the superstability for cubic functional equation by using the fixed point alternative theorem. As a consequence, we show that the cubic m...
متن کاملTamagawa Numbers of Diagonal Cubic Surfaces of Higher Rank
We consider diagonal cubic surfaces defined by an equation of the form ax + by + cz + dt = 0. Numerically, one can find all rational points of height 6 B for B in the range of up to 10 , thanks to a program due to D. J. Bernstein. On the other hand, there are precise conjectures concerning the constants in the asymptotics of rational points of bounded height due to Manin, Batyrev and the author...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1989
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-53-3-217-250