Zeros of holomorphic functions in balls
نویسندگان
چکیده
منابع مشابه
SINGULARITIES AND ZEROS OF HOLOMORPHIC FUNCTIONS Contents
So far, our focus of study has been holomorphic functions. We will now concentrate on understanding points where functions are not holomorphic. In particular, we want to generalize our understanding of the behavior of f(z) = 1/z near z = 0 to a broader range of functions, and eventually prove interesting theorems about those functions. In particular, we will prove a generalization of Cauchy’s T...
متن کاملCounting zeros of holomorphic functions of exponential growth
We consider the number of zeros of holomorphic functions in a bounded domain that depend on a small parameter and satisfy an exponential upper bound near the boundary of the domain and similar lower bounds at finitely many points along the boundary. Roughly the number of such zeros is (2πh)−1 times the integral over the domain of the laplacian of the exponent of the dominating exponential. Such...
متن کاملReal zeros of holomorphic Hecke cusp forms
This note is concerned with the zeros of holomorphic Hecke cusp forms of large weight on the modular surface. The zeros of such forms are symmetric about three geodesic segments and we call those zeros that lie on these segments, real. Our main results give estimates for the number of real zeros as the weight goes to infinity. Mathematics Subject Classification (2010). Primary: 11F11, 11F30. Se...
متن کاملFixed points of holomorphic transformations of operator balls
A new technique for proving fixed point theorems for families of holomorphic transformations of operator balls is developed. One of these theorems is used to show that a ∗Supported by St. John’s University Summer Support of Research Program
متن کاملGrowth of Balls of Holomorphic Sections and Energy at Equilibrium
Let L be a big line bundle on a compact complex manifold X. Given a non-pluripolar compact subset K of X and the weight φ of a continuous Hermitian metric e on L, we define the energy at equilibrium of (K,φ) as the Aubin-Mabuchi energy of the extremal psh weight associated to (K,φ). We prove the differentiability of the energy at equilibrium with respect to φ, and we show that this energy descr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1976
ISSN: 1385-7258
DOI: 10.1016/1385-7258(76)90009-3