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age 29
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seen Dec 27 '13 at 8:10

I am a PhD student at Mathematics Department.


Oct
28
accepted $\sum_{x \in \mathbb Z_9}w^{x^2-cx}=?$,where $c \in \mathbb Z_9$ and $w=e^{2\pi i/9}$
Oct
27
comment $\sum_{x \in \mathbb Z_9}w^{x^2-cx}=?$,where $c \in \mathbb Z_9$ and $w=e^{2\pi i/9}$
This seems precisely true to me but considering the finite field case I doupted a little. Actually, in finite field case this equals to an expression which includes Gauss sum. The answer is always $p$, seems so perfect...
Oct
26
comment $\sum_{x \in \mathbb Z_9}w^{x^2-cx}=?$,where $c \in \mathbb Z_9$ and $w=e^{2\pi i/9}$
Any useful referances to solve this are welcome and can be accepted as an answer.
Oct
26
comment $\sum_{x \in \mathbb Z_9}w^{x^2-cx}=?$,where $c \in \mathbb Z_9$ and $w=e^{2\pi i/9}$
How to calculate the last sum easily?
Oct
26
comment $\sum_{x \in \mathbb Z_9}w^{x^2-cx}=?$,where $c \in \mathbb Z_9$ and $w=e^{2\pi i/9}$
Actually, the problem is given not only for $Z_9$. The sum is over $\mahbb Z_{p^2}$ where $p$ is a prime number. But my aim is to understand for a small set first. I thought to split into two pieces as the sum over the multiplicative group and the other
Oct
26
asked $\sum_{x \in \mathbb Z_9}w^{x^2-cx}=?$,where $c \in \mathbb Z_9$ and $w=e^{2\pi i/9}$
Oct
14
accepted Solve $r=(p-1)+pr_1+p^2r_2$ for $r_1$ and $r_2$ when $r(p-1) \equiv 1$ (mod $p^3$)
Oct
14
comment Solve $r=(p-1)+pr_1+p^2r_2$ for $r_1$ and $r_2$ when $r(p-1) \equiv 1$ (mod $p^3$)
Actually, for $r \in \mathbb Z_{p}$ $r\equiv p-1 $ (mod $p$) and for $r \in \mathbb Z_{p^2}$ $r\equiv (p-1)+p(p-2) $ (mod $p^2$). However, for this case $r \neq (p-1)+p(p-2)+p(p-3)$ as we would expect
Oct
14
asked Solve $r=(p-1)+pr_1+p^2r_2$ for $r_1$ and $r_2$ when $r(p-1) \equiv 1$ (mod $p^3$)
Oct
14
comment Is $\sum_{c \notin \mathbb Z_q}\psi(c)-\sum_{c \notin \mathbb Z_q}\psi(c^n)$ an integer?
thank you. But I did not clearly understand why it is integer if I take the sum over $\mathbb Z_q^{\times}$
Oct
13
revised Is $\sum_{c \notin \mathbb Z_q}\psi(c)-\sum_{c \notin \mathbb Z_q}\psi(c^n)$ an integer?
fixed
Oct
13
comment Is $\sum_{c \notin \mathbb Z_q}\psi(c)-\sum_{c \notin \mathbb Z_q}\psi(c^n)$ an integer?
I fixed the question. It is changed now... Sorry about the syntax..
Oct
13
comment Is $\sum_{c \notin \mathbb Z_q}\psi(c)-\sum_{c \notin \mathbb Z_q}\psi(c^n)$ an integer?
I fixed the question. Sorry about that...
Oct
13
revised Is $\sum_{c \notin \mathbb Z_q}\psi(c)-\sum_{c \notin \mathbb Z_q}\psi(c^n)$ an integer?
corrected
Oct
13
asked Is $\sum_{c \notin \mathbb Z_q}\psi(c)-\sum_{c \notin \mathbb Z_q}\psi(c^n)$ an integer?
Oct
8
comment sum of $p$th roots of unity
We can think $ \sum_{x \in \mathbb Z_p}e^{\pi irk^2/p}=\sum_{x \in \mathbb Z_p}e^{2\pi irk^2/2p}$ and then have a solution according to the referance that user8268 has given previously. $r$ being odd or even does not change anything as $r/2$ mod p is well defined. Thanks for the comments
Oct
5
comment sum of $p$th roots of unity
@anon So, then could you please write the answer of the sum?
Oct
5
comment sum of $p$th roots of unity
@user8268 In the web site the given sum has $2\pi i$ in the numerator. SO, it is a little different from mine...
Oct
5
asked sum of $p$th roots of unity
Jun
5
accepted Is the number of quadratic nonresidues modulo $p^2$, greater than the number of quadratic residues modulo $p^2$?