Small solutions of quadratic congruences
Glasgow mathematical journal, Tome 26 (1985), pp. 87-93
Voir la notice de l'article provenant de la source Cambridge University Press
Let Q(x) = Q(x1, ..., xn)∈Z[x1, ..., xn] be a quadratic form. We investigate the size of the smallest non-zero solution of the congruence Q(x)≡0 (mod q). We seek a bound Bn(q), independent of Q, such that there is always a non-zero solution satisfyingThe form gives the trivial lower bound Bn(q)≥(q/n)1⁄2 for all q and n, since if x≠0 and q∣ Q(x), then Q(x)≥q.
Heath-Brown, D. R. Small solutions of quadratic congruences. Glasgow mathematical journal, Tome 26 (1985), pp. 87-93. doi: 10.1017/S0017089500006091
@article{10_1017_S0017089500006091,
author = {Heath-Brown, D. R.},
title = {Small solutions of quadratic congruences},
journal = {Glasgow mathematical journal},
pages = {87--93},
year = {1985},
volume = {26},
doi = {10.1017/S0017089500006091},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006091/}
}
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