- Analytic Number Theory
- Chebyshev functions
- Complex Analysis
- Dirichlet product
- Dirichlet series
- Divisor function
- Euler's totient function
- Little Picard theorem
- Möbius function
- Multiplicative functions
- Prime number theorem
- Ramanujan's sum
- Riemann zeta function
- Summation by parts
- Uncategorized
- Von Mangoldt function
abscissa of convergence Blaschke factors Borel-Carathéodory lemma bounds Cauchy's theorem characteristic function of divisors Chebyshev function Dirichlet series divisor function entire function Euler's totient function holomorphic function Jensen's inequality Kronecker's lemma Menon's identity Möbius function Picard theorem prime number theorem Ramanujan's sum Riemann zeta function summation by parts units zero-free region
Category Archives: Little Picard theorem
Little Picard theorem
In this article we prove the little Picard theorem assuming the existence of a nonconstant holomorphic function $\lambda : \mathbb{C} \backslash \{0, 1\} \to \mathbb{C}$ which satisifies $\text{Re} \lambda(z) \leq 0$. In the proof below we will repeatedly use the … Continue reading