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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6220 • Complex Analysis

Fall 2021 • Question 1

Question

Math 6220 • Complex Analysis Fall 2021 • Question 1

Prove that if \((f,B(0,1))\) is a function element, \(\{(g_t,U_t)\}_{t\in [0,1]}\) and \(\{(h_t,V_t)\}_{t\in [0,1]}\) are analytic continuations of \((f,B(0,1))\) along the curve \(\phi : [0,1]\to \mathbb {C}\) defined by \(\phi (t)=4t+it\) then \(g_1=h_1\) in a neighborhood of \(4+i\).

Raw LaTeX

Prove that if \((f,B(0,1))\) is a function element, \(\{(g_t,U_t)\}_{t\in[0,1]}\) and
\(\{(h_t,V_t)\}_{t\in[0,1]}\) are analytic continuations of \((f,B(0,1))\) along the curve \(\phi:
[0,1]\to\mathbb{C}\) defined by \(\phi(t)=4t+it\) then \(g_1=h_1\) in a neighborhood of \(4+i\).

Topic Tags

Analytic Continuation and Monodromy