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math.NT2014★ 7 cited
Genus Periods, Genus Points and Congruent Number Problem
Ye Tian, Xinyi Yuan, Shouwu Zhang
In this paper, based on an ideal of Tian, we establish a new sufficient condition for a positive integer to be a congruent number in terms of Legendre symbols of prime factors of t…
math.NT2014★ 1 cited
Effective Bounds of Linear Series on Algebraic Varieties and Arithmetic Varieties
Xinyi Yuan, Tong Zhang
In this paper, we prove effective upper bounds for effective sections of line bundles on projective varieties and hermitian line bundles on arithmetic varieties in terms of the vol…