Chebyshev’s bias for analytic L-functions

Analytic Approximation of Matrix Functions in L

We consider the problem of approximation of matrix functions of class L on the unit circle by matrix functions analytic in the unit disk in the norm of L, 2 ≤ p < ∞. For an m × n matrix function Φ in L, we consider the Hankel operator HΦ : H(C) → H −(C), 1/p + 1/q = 1/2. It turns out that the space of m × n matrix functions in L splits into two subclasses: the set of respectable matrix function...

Analytic p-adic L-functions for GL2: a summary

One of the most subtle and important invariants of a modular form f is its L-function L(s, f). For holomorphic modular forms, the basic analytic properties of their L-functions were established by Hecke, with Maass treating the real-analytic forms; their construction gave L(s, f) as a Mellin transform of f . In the early 70s, the existence of p-adic L-functions associated with classical modular...

On Sandwich theorems for certain classes of analytic functions

The purpose of this present paper is to derive some subordination and superordination results for certain analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

Application of the Norm Estimates for Univalence of Analytic Functions

By using norm estimates of the pre-Schwarzian derivatives for certain family of analytic functions, we shall give simple sufficient conditions for univalence of analytic functions.

The Fekete-Szego Coefficient Functional for Transforms of Analytic Functions