Sums of three squares under congruence condition modulo a prime
نویسندگان
چکیده
منابع مشابه
Subset Sums modulo a Prime
Let Zp be the finite field of prime order p and A be a subset of Zp. We prove several sharp results about the following two basic questions: (1) When can one represent zero as a sum of distinct elements of A ? (2) When can one represent every element of Zp as a sum of distinct elements of A ?
متن کاملOn a Congruence modulo a Prime
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive o...
متن کاملAdding distinct congruence classes modulo a prime
The Cauchy-Davenport theorem states that if A and B are nonempty sets of congruence classes modulo a prime p, and if |A| = k and |B| = l, then the sumset A + B contains at least min(p, k + l − 1) congruence classes. It follows that the sumset 2A contains at least min(p, 2k − 1) congruence classes. Erdős and Heilbronn conjectured 30 years ago that there are at least min(p, 2k − 3) congruence cla...
متن کاملEnumeration of Power Sums Modulo A Prime
We consider, for odd primes p, the function N(p, m, e) which equals the number of subsets SC{1 ,...,p 1) with the property that &sxm = OL (modp). We obtain a closed form expression for N(p, m, IX). We give simple explicit formulas for N(p, 2, CZ) (which in some casea involve class numbers and fundamental units), and show that for a fixed m, the diffenx~ce between N(p, m, a) and its average valu...
متن کاملExponential Sums modulo Prime Powers
where p is a prime power with m ≥ 2, χ is a multiplicative character (mod p), epm(·) is the additive character, epm(x) = e 2πix pm , and f, g are rational functions with integer coefficients. It is understood, that the sum is only over values of x for which g and f and both defined as functions on Z/(p), and g is nonzero (mod p). The sum is trivial if f and g are both constants, so we shall alw...
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: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.07.011