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Search: MSC category 14H52 ( Elliptic curves [See also 11G05, 11G07, 14Kxx] )

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1. CMB 2011 (vol 55 pp. 850)

Shparlinski, Igor E.; Stange, Katherine E.
 Character Sums with Division Polynomials We obtain nontrivial estimates of quadratic character sums of division polynomials $\Psi_n(P)$, $n=1,2, \dots$, evaluated at a given point $P$ on an elliptic curve over a finite field of $q$ elements. Our bounds are nontrivial if the order of $P$ is at least $q^{1/2 + \varepsilon}$ for some fixed $\varepsilon > 0$. This work is motivated by an open question about statistical indistinguishability of some cryptographically relevant sequences that was recently brought up by K. Lauter and the second author. Keywords:division polynomial, character sumCategories:11L40, 14H52

2. CMB 2005 (vol 48 pp. 428)

Miyamoto, Roland; Top, Jaap
 Reduction of Elliptic Curves in Equal Characteristic~3 (and~2) and fibre type for elliptic curves over discrete valued fields of equal characteristic~3. Along the same lines, partial results are obtained in equal characteristic~2. Categories:14H52, 14K15, 11G07, 11G05, 12J10

3. CMB 2000 (vol 43 pp. 239)

Yu, Gang
 On the Number of Divisors of the Quadratic Form $m^2+n^2$ For an integer $n$, let $d(n)$ denote the ordinary divisor function. This paper studies the asymptotic behavior of the sum $$S(x) := \sum_{m\leq x, n\leq x} d(m^2 + n^2).$$ It is proved in the paper that, as $x \to \infty$, $$S(x) := A_1 x^2 \log x + A_2 x^2 + O_\epsilon (x^{\frac32 + \epsilon}),$$ where $A_1$ and $A_2$ are certain constants and $\epsilon$ is any fixed positive real number. The result corrects a false formula given in a paper of Gafurov concerning the same problem, and improves the error $O \bigl( x^{\frac53} (\log x)^9 \bigr)$ claimed by Gafurov. Keywords:divisor, large sieve, exponential sumsCategories:11G05, 14H52
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