作者：GOLDBERG, LR
作者单位：City University of New York (CUNY) System; Brooklyn College (CUNY)
摘要：We estimate the multiplier lambda of a repelling fixed point with rational rotation number for a polynomial in one complex variable. We show that a canonical branch of the logarithm of lambda lies in a small disk tangent to the imaginary axis. The radius of the disk is determined by the degree of the polynomial, the rotation number of the fixed point and the escape rates and external arguments of the critical values.
作者：BUSER, P; SARNAK, P
作者单位：Princeton University
摘要：Riemann showed that a period matrix of a compact Riemann surface of genus g greater-than-or-equal-to 1 satisfies certain relations. We give a further simple combinatorial property, related to the length of the shortest non-zero lattice vector, satisfied by such a period matrix, see (1.13). In particular, it is shown that for large genus the entire locus of Jacobians lies in a very small neighborhood of the boundary of the space of principally polarized abelian varieties. We apply this to the p...
