I What are the Zeta Function and the Riemann Hypothesis?

  • I
  • Thread starter Thread starter PeaceMartian
  • Start date Start date
  • Tags Tags
    Function Riemann
AI Thread Summary
The zeta function is a complex function that plays a crucial role in number theory, particularly in understanding the distribution of prime numbers. The Riemann Hypothesis posits that all non-trivial zeros of the zeta function lie on a specific line in the complex plane, which has significant implications for mathematics. The discussion emphasizes the historical importance and ongoing relevance of these concepts in mathematical research. Resources are provided for further exploration of the zeta function and the Riemann Hypothesis. Understanding these topics is essential for grasping advanced mathematical theories.
PeaceMartian
Messages
2
Reaction score
2
TL;DR Summary
What is the zeta function.
What is the zeta function and the Riemann hypothesis.
 
Mathematics news on Phys.org

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Imaginary Pythagoras'

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Similar threads

Insights The Extended Riemann Hypothesis and Ramanujan’s Sum
Replies
3
Views
2K
Insights The History and Importance of the Riemann Hypothesis
Replies
0
Views
2K
B Does this help solve the Riemann Hypothesis?
Replies
4
Views
2K
Insights Computing the Riemann Zeta Function Using Fourier Series
Replies
5
Views
3K
I Connection of zeta to primes: less Euler than error or L-functions?
Replies
2
Views
2K
I Hausdorff dimension of Riemann zeta function assuming RH
Replies
11
Views
3K
I Riemann zeta: regularization and universality
Replies
1
Views
2K
B Isn't the Riemann Hypothesis just a convention?
Replies
25
Views
4K
B How does the Riemann Hypothesis/Riemann Zeta function even work?
Replies
17
Views
974
A Paper About the Riemann Zeta Function
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top