# Qiang Zhang

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bio website prime.sdu.edu.cn/… location Jinan, China age 26 member for 2 years, 8 months seen 17 hours ago profile views 129

I am currently a graduate student specialized in analytic number theory at Shandong University. My research interests are in Riemann zeta function and automorphic forms.

# 13 Questions

 9 Why does the equation $x^2-82y^2=\pm2$ have solutions in every $\mathbb{Z}_p$ but not in $\mathbb{Z}$? 7 The number of solutions of the equation $x^n+y^n=1$ over $\mathbb{Z}_p$ with $\mathbb{Z}_p=\{\alpha\in \mathbb{Q}_p:|\alpha|_p\le 1\}$. 7 Compute the Unit and Class Number of a pure cubic field $\mathbb{Q}(\sqrt[3]{6})$ 6 The generalized Euler's function in number field for ideal $\mathfrak{a}$ 4 Find an integer $n$ such that $\mathbb{Z}[\frac{1}{20},\frac{1}{32}]=\mathbb{Z}[\frac{1}{n}]$.

# 404 Reputation

 +10 $p$ a prime, $p \equiv 3 \pmod 4$. Prove that $\frac{p-1}{2}! \equiv \pm 1 \pmod p$ +10 Compute the Unit and Class Number of a pure cubic field $\mathbb{Q}(\sqrt[3]{6})$ +5 The number of solutions of the equation $x^n+y^n=1$ over $\mathbb{Z}_p$ with $\mathbb{Z}_p=\{\alpha\in \mathbb{Q}_p:|\alpha|_p\le 1\}$. +5 Why is the restricted direct product topology on the idele group stronger than the topology induced by the adele group?

 1 $p$ a prime, $p \equiv 3 \pmod 4$. Prove that $\frac{p-1}{2}! \equiv \pm 1 \pmod p$ 1 Question about Cyclic Group 1 Normal extension with simple, not cyclic Galois group

# 15 Tags

 1 algebraic-number-theory × 9 0 valuation-theory × 4 1 number-theory × 3 0 p-adic-number-theory × 2 1 prime-numbers 0 analytic-number-theory × 2 1 group-theory 0 summation 1 discrete-mathematics 0 sequences-and-series

# 2 Accounts

 Mathematics 404 rep 211 MathOverflow 101 rep 2