Enhance Your Calculus Skills with Recommended Books for Riemann Zeta Function

[sparsh12]

i am interested in Riemann zeta function. i am in a high school.
i have good hold over calculus(at least what's required for physics).
Would Tom Apostle's Calculus I be good to further improve my skills.

What should i do next?
Real Analysis or Complex Analysis or directly analytic number theory?

Are L Ahlfors' complex analysis and Analytic Number Theory by Tom Apostle good at my level?

By the way, has Riemann hypothesis been proved?
have a look at http://www.coolissues.com/mathematics/Zeta/zeta.htm.

There are several pages by same author, on several unsolved problems,here:
http://www.coolissues.com/mathematics/Zeta/zeta.htm

 

[SteveL27]

i am interested in Riemann zeta function. i am in a high school.
i have good hold over calculus(at least what's required for physics).
Would Tom Apostle's Calculus I be good to further improve my skills.

What should i do next?
Real Analysis or Complex Analysis or directly analytic number theory?

Are L Ahlfors' complex analysis and Analytic Number Theory by Tom Apostle good at my level?

Real analysis first, then complex analysis, then basic number theory, then analytic number theory. And a strong grounding in multivariable calculus will help a lot with complex variables, so don't skip that.

If you're interested in analytic number theory, there's a book you can start reading right now and grow into as you learn more. Hardy and Wright. It's a classic.

https://www.amazon.com/dp/0199219869/?tag=pfamazon01-20

 

[Norwegian]

Hi sparsh12, I wish you all the best in your mathematical endeavors.

Just want to mention that the links you included are by a mathematical crank. There are lots of them out there, doing their own "research", and producing results, that if true, would cause well establish facts to be wrong. James Constant is a quite sophisticated crank, he knows a fair amount of math, he can write coherently, but his conclusions are just wrong. When a crank gets a result that contradicts hundreds of years of work by the best minds on the planet, they do not pause and ponder "where did I go wrong?", instead they have an urge to inform us all about their discoveries. I Just remembered that cranky stuff isn't allowed here in the forum, so I should stop.

 

[lostcauses10x]

There is a lot of valid info on the net as well as invalid info.

Keep learning and reading. So far no proof of RH that I know of exists.

 

[blue_raver22]

I am glad to hear that you are interested in Riemann zeta function and have a good understanding of calculus. To further enhance your skills, I would recommend Tom Apostle's Calculus I as it covers the basic concepts of calculus that are necessary for understanding the Riemann zeta function.

As for what to do next, it depends on your interests and goals. Real analysis and complex analysis are both important branches of mathematics that are closely related to the Riemann zeta function. If you are interested in pursuing a career in mathematics or physics, it would be beneficial to study both of these subjects. Analytic number theory is also closely related to the Riemann zeta function, but it may be more advanced for a high school student. I would recommend exploring all three subjects and seeing which one interests you the most.

As for specific books, L Ahlfors' complex analysis and Analytic Number Theory by Tom Apostle are both excellent choices at your level. They cover the necessary topics and provide a good foundation for further study.

I am not able to comment on the proof of the Riemann hypothesis as it is still an unsolved problem in mathematics. However, I would encourage you to continue exploring the Riemann zeta function and other unsolved problems in mathematics. It is through curiosity and exploration that new discoveries are made.

I also recommend checking out the resources provided in the link you shared. They seem to be a good starting point for learning about the Riemann zeta function and other unsolved problems in mathematics.

In summary, I encourage you to continue your interest in the Riemann zeta function and explore other related topics in mathematics. With dedication and hard work, you can further enhance your skills and potentially make contributions to the field of mathematics. Keep learning and never stop asking questions. Best of luck on your mathematical journey!