Sums of almost equal squares of primes
نویسندگان
چکیده
منابع مشابه
Sums of almost equal prime squares
In this short note, we prove that almost all integers N satisfying N ≡ 3 (mod 24) and 5 -N or N ≡ 4 (mod 24) is the sum of three or four almost equal prime squares, respectively: N = p21 + · · ·+ p 2 j with |pi − (N/j) 1/2| ≤ N1/2−9/80+ε for j = 3 or 4 and 1 ≤ i ≤ j.
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In 1997 K. Ono and K. Soundararajan [Invent. Math. 130(1997)] proved that under the generalized Riemann hypothesis any positive odd integer greater than 2719 can be represented by the famous Ramanujan form x2 + y2+10z2; equivalently the form 2x+5y+4Tz represents all integers greater than 1359, where Tz denotes the triangular number z(z+1)/2. Given positive integers a, b, c we employ modular for...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2012
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2011.12.004