Are these enough to research in Algebraic Number Theory? [closed]

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$ text{Algebraic Number Theory:}$

To do research in Algebraic Number Theory what are the essential topics to know?

I have basic knowledge in Abstract Algebra, Topology and Analysis as well as the number fields $ mathbb{Q}, mathbb{R}, mathbb{C}$.

I do not have much knowledge in Analytic Number Theory.

Are these enough to research in Algebraic Number Theory?

If somebody can give advice me regarding the above questions.

Also please tell me some best book in Algebraic Number Theory.

Thanks,

edited Nov 22 at 14:53

asked Nov 22 at 13:49

arifamath

845

closed as off-topic by José Carlos Santos, Watson, amWhy, rtybase, davidlowryduda♦ Nov 24 at 14:38

This question appears to be off-topic. The users who voted to close gave this specific reason:

"Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – José Carlos Santos, davidlowryduda

If this question can be reworded to fit the rules in the help center, please edit the question.

3

If by "usual knowledge" of Abstract algebra you mean Basic Group Theory, Ring Theory (in particular polynomial rings), Fields extensions and basic Galois Theory, and of course also Linear Algebra, then yes: that seems to be enough to tackle basic Algebraic Number Theory. Now, for research I'd say much more is needed: some basic Analytic Number Theory and Complex Analysis will surely help.
– DonAntonio
Nov 22 at 14:10

1

I think you will need number theory also.
– tarit goswami
Nov 22 at 15:18

1

From my student perspective I'd say in number theory there are two kind of papers : those with a lot of asymptotic estimates in order to derive and refine some error terms in analytic number theory, and those with a lot of theoretical objects appearing in the theory of Galois representations, automorphic forms, varieties, cohomology, class field theory.
– reuns
Nov 22 at 20:10

1

I'd recommend trying 1 or 2 books on Algebraic Number Theory (there are PDF's online) and ... if there is something you don't understand in those books, that will be the gap you have to cover.
– rtybase
Nov 22 at 22:24

1

Yes I have some book on ANT . For example, a book by Neukric, a book by F. Oggier, a book by M. Ram Murty.
– arifamath
Nov 22 at 22:31

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show 1 more comment

up vote
3
down vote

favorite

$ text{Algebraic Number Theory:}$

To do research in Algebraic Number Theory what are the essential topics to know?

I have basic knowledge in Abstract Algebra, Topology and Analysis as well as the number fields $ mathbb{Q}, mathbb{R}, mathbb{C}$.

I do not have much knowledge in Analytic Number Theory.

Are these enough to research in Algebraic Number Theory?

If somebody can give advice me regarding the above questions.

Also please tell me some best book in Algebraic Number Theory.

Thanks,

edited Nov 22 at 14:53

asked Nov 22 at 13:49

arifamath

845

closed as off-topic by José Carlos Santos, Watson, amWhy, rtybase, davidlowryduda♦ Nov 24 at 14:38

This question appears to be off-topic. The users who voted to close gave this specific reason:

"Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – José Carlos Santos, davidlowryduda

If this question can be reworded to fit the rules in the help center, please edit the question.

3

If by "usual knowledge" of Abstract algebra you mean Basic Group Theory, Ring Theory (in particular polynomial rings), Fields extensions and basic Galois Theory, and of course also Linear Algebra, then yes: that seems to be enough to tackle basic Algebraic Number Theory. Now, for research I'd say much more is needed: some basic Analytic Number Theory and Complex Analysis will surely help.
– DonAntonio
Nov 22 at 14:10

1

I think you will need number theory also.
– tarit goswami
Nov 22 at 15:18

1

From my student perspective I'd say in number theory there are two kind of papers : those with a lot of asymptotic estimates in order to derive and refine some error terms in analytic number theory, and those with a lot of theoretical objects appearing in the theory of Galois representations, automorphic forms, varieties, cohomology, class field theory.
– reuns
Nov 22 at 20:10

1

I'd recommend trying 1 or 2 books on Algebraic Number Theory (there are PDF's online) and ... if there is something you don't understand in those books, that will be the gap you have to cover.
– rtybase
Nov 22 at 22:24

1

Yes I have some book on ANT . For example, a book by Neukric, a book by F. Oggier, a book by M. Ram Murty.
– arifamath
Nov 22 at 22:31

|
show 1 more comment

up vote
3
down vote

favorite

$ text{Algebraic Number Theory:}$

To do research in Algebraic Number Theory what are the essential topics to know?

I have basic knowledge in Abstract Algebra, Topology and Analysis as well as the number fields $ mathbb{Q}, mathbb{R}, mathbb{C}$.

I do not have much knowledge in Analytic Number Theory.

Are these enough to research in Algebraic Number Theory?

If somebody can give advice me regarding the above questions.

Also please tell me some best book in Algebraic Number Theory.

Thanks,

edited Nov 22 at 14:53

asked Nov 22 at 13:49

arifamath

845

$ text{Algebraic Number Theory:}$

To do research in Algebraic Number Theory what are the essential topics to know?

I have basic knowledge in Abstract Algebra, Topology and Analysis as well as the number fields $ mathbb{Q}, mathbb{R}, mathbb{C}$.

I do not have much knowledge in Analytic Number Theory.

Are these enough to research in Algebraic Number Theory?

If somebody can give advice me regarding the above questions.

Also please tell me some best book in Algebraic Number Theory.

Thanks,

number-theory algebraic-number-theory algebraic-numbers

edited Nov 22 at 14:53

asked Nov 22 at 13:49

arifamath

845

edited Nov 22 at 14:53

asked Nov 22 at 13:49

arifamath

845

edited Nov 22 at 14:53

asked Nov 22 at 13:49

arifamath

845

asked Nov 22 at 13:49

arifamath

845

asked Nov 22 at 13:49

arifamath

845

closed as off-topic by José Carlos Santos, Watson, amWhy, rtybase, davidlowryduda♦ Nov 24 at 14:38

This question appears to be off-topic. The users who voted to close gave this specific reason:

"Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – José Carlos Santos, davidlowryduda

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by José Carlos Santos, Watson, amWhy, rtybase, davidlowryduda♦ Nov 24 at 14:38

This question appears to be off-topic. The users who voted to close gave this specific reason:

"Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – José Carlos Santos, davidlowryduda

If this question can be reworded to fit the rules in the help center, please edit the question.

3

If by "usual knowledge" of Abstract algebra you mean Basic Group Theory, Ring Theory (in particular polynomial rings), Fields extensions and basic Galois Theory, and of course also Linear Algebra, then yes: that seems to be enough to tackle basic Algebraic Number Theory. Now, for research I'd say much more is needed: some basic Analytic Number Theory and Complex Analysis will surely help.
– DonAntonio
Nov 22 at 14:10

1

I think you will need number theory also.
– tarit goswami
Nov 22 at 15:18

1

From my student perspective I'd say in number theory there are two kind of papers : those with a lot of asymptotic estimates in order to derive and refine some error terms in analytic number theory, and those with a lot of theoretical objects appearing in the theory of Galois representations, automorphic forms, varieties, cohomology, class field theory.
– reuns
Nov 22 at 20:10

1

I'd recommend trying 1 or 2 books on Algebraic Number Theory (there are PDF's online) and ... if there is something you don't understand in those books, that will be the gap you have to cover.
– rtybase
Nov 22 at 22:24

1

Yes I have some book on ANT . For example, a book by Neukric, a book by F. Oggier, a book by M. Ram Murty.
– arifamath
Nov 22 at 22:31

|
show 1 more comment

3

If by "usual knowledge" of Abstract algebra you mean Basic Group Theory, Ring Theory (in particular polynomial rings), Fields extensions and basic Galois Theory, and of course also Linear Algebra, then yes: that seems to be enough to tackle basic Algebraic Number Theory. Now, for research I'd say much more is needed: some basic Analytic Number Theory and Complex Analysis will surely help.
– DonAntonio
Nov 22 at 14:10

1

I think you will need number theory also.
– tarit goswami
Nov 22 at 15:18

1

From my student perspective I'd say in number theory there are two kind of papers : those with a lot of asymptotic estimates in order to derive and refine some error terms in analytic number theory, and those with a lot of theoretical objects appearing in the theory of Galois representations, automorphic forms, varieties, cohomology, class field theory.
– reuns
Nov 22 at 20:10

1

I'd recommend trying 1 or 2 books on Algebraic Number Theory (there are PDF's online) and ... if there is something you don't understand in those books, that will be the gap you have to cover.
– rtybase
Nov 22 at 22:24

1

Yes I have some book on ANT . For example, a book by Neukric, a book by F. Oggier, a book by M. Ram Murty.
– arifamath
Nov 22 at 22:31

If by "usual knowledge" of Abstract algebra you mean Basic Group Theory, Ring Theory (in particular polynomial rings), Fields extensions and basic Galois Theory, and of course also Linear Algebra, then yes: that seems to be enough to tackle basic Algebraic Number Theory. Now, for research I'd say much more is needed: some basic Analytic Number Theory and Complex Analysis will surely help.
– DonAntonio
Nov 22 at 14:10

I think you will need number theory also.
– tarit goswami
Nov 22 at 15:18

From my student perspective I'd say in number theory there are two kind of papers : those with a lot of asymptotic estimates in order to derive and refine some error terms in analytic number theory, and those with a lot of theoretical objects appearing in the theory of Galois representations, automorphic forms, varieties, cohomology, class field theory.
– reuns
Nov 22 at 20:10

I'd recommend trying 1 or 2 books on Algebraic Number Theory (there are PDF's online) and ... if there is something you don't understand in those books, that will be the gap you have to cover.
– rtybase
Nov 22 at 22:24

Yes I have some book on ANT . For example, a book by Neukric, a book by F. Oggier, a book by M. Ram Murty.
– arifamath
Nov 22 at 22:31

|
show 1 more comment

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