Results/topics on p-adic number theory analysis understandable by undergraduates
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I've been reading about p-adic analysis lately, and am interested to work on a specific topic about it for my undergraduate thesis. However, almost all dissertations I've read online are too hard to grasp for an undergraduate.
Topics on p-adic hodge theory, p-adic etale cohomology, p-adic L functions, p-adic application on number theory cryptography, and perfectoid spaces are some interesting topics on p-adic. But those are quite out of reach for most of us, I would like to know if there had been any interesting results about those that could be stated and/or worked on by an undergraduate?
If not, could you suggest any results/consequences on p-adic workable by an undergraduate?
Thank you!
p-adic-number-theory
asked Nov 28 '18 at 0:14
Jonelle YuJonelle Yu
1776
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add a comment |
$begingroup$
I've been reading about p-adic analysis lately, and am interested to work on a specific topic about it for my undergraduate thesis. However, almost all dissertations I've read online are too hard to grasp for an undergraduate.
Topics on p-adic hodge theory, p-adic etale cohomology, p-adic L functions, p-adic application on number theory cryptography, and perfectoid spaces are some interesting topics on p-adic. But those are quite out of reach for most of us, I would like to know if there had been any interesting results about those that could be stated and/or worked on by an undergraduate?
If not, could you suggest any results/consequences on p-adic workable by an undergraduate?
Thank you!
p-adic-number-theory
asked Nov 28 '18 at 0:14
Jonelle YuJonelle Yu
1776
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$begingroup$
how about Dwork's proof of the rationality of the zeta function? See, for instance, amazon.com/Numbers-Analysis-Zeta-Functions-Graduate-Mathematics/…
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– peter a g
Nov 28 '18 at 1:24
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And here is a version of the previous on line:citeseerx.ist.psu.edu/viewdoc/…
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– peter a g
Nov 28 '18 at 1:28
1
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Maybe this will help: mathoverflow.net/q/81342. A list of elementary results using p-adic analysis.
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– twnly
Nov 28 '18 at 2:33
add a comment |
$begingroup$
I've been reading about p-adic analysis lately, and am interested to work on a specific topic about it for my undergraduate thesis. However, almost all dissertations I've read online are too hard to grasp for an undergraduate.
Topics on p-adic hodge theory, p-adic etale cohomology, p-adic L functions, p-adic application on number theory cryptography, and perfectoid spaces are some interesting topics on p-adic. But those are quite out of reach for most of us, I would like to know if there had been any interesting results about those that could be stated and/or worked on by an undergraduate?
If not, could you suggest any results/consequences on p-adic workable by an undergraduate?
Thank you!
p-adic-number-theory
asked Nov 28 '18 at 0:14
Jonelle YuJonelle Yu
1776
$endgroup$
I've been reading about p-adic analysis lately, and am interested to work on a specific topic about it for my undergraduate thesis. However, almost all dissertations I've read online are too hard to grasp for an undergraduate.
Topics on p-adic hodge theory, p-adic etale cohomology, p-adic L functions, p-adic application on number theory cryptography, and perfectoid spaces are some interesting topics on p-adic. But those are quite out of reach for most of us, I would like to know if there had been any interesting results about those that could be stated and/or worked on by an undergraduate?
If not, could you suggest any results/consequences on p-adic workable by an undergraduate?
Thank you!
p-adic-number-theory
p-adic-number-theory
asked Nov 28 '18 at 0:14
Jonelle YuJonelle Yu
1776
asked Nov 28 '18 at 0:14
Jonelle YuJonelle Yu
1776
asked Nov 28 '18 at 0:14
Jonelle YuJonelle Yu
1776
asked Nov 28 '18 at 0:14
Jonelle YuJonelle Yu
1776
asked Nov 28 '18 at 0:14
Jonelle YuJonelle Yu
1776
1776
$begingroup$
how about Dwork's proof of the rationality of the zeta function? See, for instance, amazon.com/Numbers-Analysis-Zeta-Functions-Graduate-Mathematics/…
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– peter a g
Nov 28 '18 at 1:24
$begingroup$
And here is a version of the previous on line:citeseerx.ist.psu.edu/viewdoc/…
$endgroup$
– peter a g
Nov 28 '18 at 1:28
1
$begingroup$
Maybe this will help: mathoverflow.net/q/81342. A list of elementary results using p-adic analysis.
$endgroup$
– twnly
Nov 28 '18 at 2:33
add a comment |
$begingroup$
how about Dwork's proof of the rationality of the zeta function? See, for instance, amazon.com/Numbers-Analysis-Zeta-Functions-Graduate-Mathematics/…
$endgroup$
– peter a g
Nov 28 '18 at 1:24
$begingroup$
And here is a version of the previous on line:citeseerx.ist.psu.edu/viewdoc/…
$endgroup$
– peter a g
Nov 28 '18 at 1:28
1
$begingroup$
Maybe this will help: mathoverflow.net/q/81342. A list of elementary results using p-adic analysis.
$endgroup$
– twnly
Nov 28 '18 at 2:33
$begingroup$
how about Dwork's proof of the rationality of the zeta function? See, for instance, amazon.com/Numbers-Analysis-Zeta-Functions-Graduate-Mathematics/…
$endgroup$
– peter a g
Nov 28 '18 at 1:24
$begingroup$
how about Dwork's proof of the rationality of the zeta function? See, for instance, amazon.com/Numbers-Analysis-Zeta-Functions-Graduate-Mathematics/…
$endgroup$
– peter a g
Nov 28 '18 at 1:24
$begingroup$
And here is a version of the previous on line:citeseerx.ist.psu.edu/viewdoc/…
$endgroup$
– peter a g
Nov 28 '18 at 1:28
$begingroup$
And here is a version of the previous on line:citeseerx.ist.psu.edu/viewdoc/…
$endgroup$
– peter a g
Nov 28 '18 at 1:28
1
1
$begingroup$
Maybe this will help: mathoverflow.net/q/81342. A list of elementary results using p-adic analysis.
$endgroup$
– twnly
Nov 28 '18 at 2:33
$begingroup$
Maybe this will help: mathoverflow.net/q/81342. A list of elementary results using p-adic analysis.
$endgroup$
– twnly
Nov 28 '18 at 2:33
add a comment |
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$begingroup$
how about Dwork's proof of the rationality of the zeta function? See, for instance, amazon.com/Numbers-Analysis-Zeta-Functions-Graduate-Mathematics/…
$endgroup$
– peter a g
Nov 28 '18 at 1:24
$begingroup$
And here is a version of the previous on line:citeseerx.ist.psu.edu/viewdoc/…
$endgroup$
– peter a g
Nov 28 '18 at 1:28
1
$begingroup$
Maybe this will help: mathoverflow.net/q/81342. A list of elementary results using p-adic analysis.
$endgroup$
– twnly
Nov 28 '18 at 2:33