On sums of two and three roots of unity
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DOI: 10.1016/j.jnt.2018.03.017
Abstract: Abstract Let α ≠ 0 be a sum of some k distinct Nth roots of unity, where 2 ≤ k N . In 1986, Myerson raised the following two problems. How small can | α… read more here.
Keywords: sums two; two three; three roots; roots unity ... See more keywords
Fractional moments of L$L$ ‐functions and sums of two squares in short intervals
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DOI: 10.1112/mtk.70047
Abstract: Let b(n)=1$b(n)=1$ if n$n$ is the sum of two perfect squares, and b(n)=0$b(n)=0$ otherwise. We study the variance of B(x)=∑n⩽xb(n)$B(x)=\sum _{n\leqslant x}b(n)$ in short intervals by relating the variance with the second moment of the… read more here.
Keywords: moments functions; two squares; fractional moments; functions sums ... See more keywords
INTERVALS BETWEEN CONSECUTIVE NUMBERS WHICH ARE SUMS OF TWO SQUARES
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DOI: 10.1112/s0025579319000299
Abstract: In this paper, we improve the moment estimates for the gaps between numbers that can be represented as a sum of two squares of integers. We consider certain sum of Bessel functions and prove the… read more here.
Keywords: numbers sums; sums two; intervals consecutive; consecutive numbers ... See more keywords
Repdigits as sums of two generalized Lucas numbers
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DOI: 10.3906/mat-2011-59
Abstract: A generalization of the well–known Lucas sequence is the k -Lucas sequence with some fixed integer k ≥ 2 . The first k terms of this sequence are 0, . . . , 0, 2,… read more here.
Keywords: generalized lucas; sums two; lucas; repdigits sums ... See more keywords