The representation of integers by positive ternary quadratic polynomials
نویسندگان
چکیده
منابع مشابه
Representation of Integers by Ternary Quadratic Forms: a Geometric Approach
In 1957 N.C. Ankeny provided a new proof of the three squares theorem using geometry of numbers. This paper generalizes Ankeny’s technique, proving exactly which integers are represented by x2 + 2y2 + 2z2 and x2 + y2 + 2z2 as well as proving su cient conditions for an integer to be represented by x2 + y2 + 3z2 and x2 + y2 + 7z2.
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The problem of determining when an integral quadratic form represents every positive integer has received much attention in recent years, culminating in the 15 and 290 Theorems of Bhargava-Conway-Schneeberger and Bhargava-Hanke. For ternary quadratic forms, there are always local obstructions, but one may ask whether there are ternary quadratic forms which represent every locally represented in...
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Following a statement of the well-known Erdős-Turán conjecture, Erdős mentioned the following even stronger conjecture: if the n-th term an of a sequence A of positive integers is bounded by αn2, for some positive real constant α, then the number of representations of n as a sum of two terms from A is an unbounded function of n. Here we show that if an differs from αn 2 (or from a quadratic pol...
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The operation of finding the limit of an infinite series has been one of the most fruitful operations of all mathematics. While this is not a group operation the theory of continuous transformation groups inaugurated by S. Lie has thrown much new light on this operation. The assumption that only two elements are combined at a time applies to continuous groups as well as to those which are disco...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2015
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.03.007