Is there a course available for the Riemann Hypothesis (RH)?

In summary: It's a great read and gives a lot of insight into the background and importance of the RH.In summary, there is a possibility that a course on the Riemann Hypothesis (RH) may be offered by a Purdue professor, but it has not been confirmed. However, there are resources available such as the book "Prime Obsession" that discuss the topic in a more approachable manner. Additionally, a paper is mentioned that delves into the structure of the zeta function, which is related to the RH.
  • #1
MathematicalPhysicist
Gold Member
4,699
371
Does someone know if there's a course offered on RH?

I mean reading the literature can be quite intimidating without some beckground before, I read somewhere that the prof from purdue (who allegedlly proved RH) was contemplating offering such a course, but didn't offer such a course.
 
Physics news on Phys.org
  • #2
If you mean to say Riemann Hypothesis by 'RH' ,here's a good book:
Prime Obsession (by J. Derbyshire).
 
  • #3
a phycisist approach to RH , is a bit simpler it use the approximate asymptotic formula

[tex] f^{-1} (x) = \sqrt (4\pi ) \frac{d^{-1/2}g(x)}{dx^{-1/2}} [/tex]

this formula is valid only for one spatial dimension (x,t) , so the conjectured WKB approximation for the inverse of the potential inside the Hamiltonian

[tex] -D^{2}+f(x) [/tex] with D meaning derivative respect to 'x' is

[tex] \pi f^{-1}(x) = \int_{0}^{x} \frac{g(t)dt}{(x-t)^{1/2}} [/tex]

with [tex] g(s)= (-i)^{1/2}\frac{ \xi ' (1/2+is)}{\xi(1/2+is)}+(i)^{1/2}\frac{ \xi ' (1/2-is)}{\xi(1/2-is)} [/tex]

since for RH [tex] g(s)= dN(s) [/tex] and [tex] N(E)= \frac{1}{\pi}Arg \xi(1/2+iE) [/tex]
 
  • #4
MathematicalPhysicist said:
Does someone know if there's a course offered on RH?

I mean reading the literature can be quite intimidating without some beckground before, I read somewhere that the prof from purdue (who allegedlly proved RH) was contemplating offering such a course, but didn't offer such a course.

I think I would be interested in working on such a project although I think it would be better titled as the zeta function and approached through a strong foundation in Complex Analysis. I'm not an expert though.
 
  • #6
Eynstone said:
If you mean to say Riemann Hypothesis by 'RH' ,here's a good book:
Prime Obsession (by J. Derbyshire).

I'll second this, just finishing it up actually.
 

1. What is RH and why is it important to study?

RH, or Relative Humidity, is the measure of how much water vapor is in the air compared to the maximum amount of water vapor that the air can hold at a given temperature. It is important to study because it affects our daily lives in various ways, such as weather patterns, human comfort, and the growth and development of plants.

2. What are the main factors that influence RH?

The main factors that influence RH include temperature, air pressure, and the amount of water vapor present in the air. Higher temperatures and lower air pressure can lead to lower RH, while lower temperatures and higher air pressure can lead to higher RH. The amount of water vapor present in the air is directly related to RH, as it is the primary measure of how saturated the air is with water vapor.

3. How is RH measured and what are the common units used?

RH is typically measured using a hygrometer, which measures the amount of water vapor in the air. The most common units used to measure RH are percentage (%), which represents the ratio of the actual amount of water vapor present to the maximum amount the air can hold at a given temperature, and grams per cubic meter (g/m3), which represents the mass of water vapor per unit volume of air.

4. What are some common applications of RH in different fields?

RH has many applications in various fields, including meteorology, agriculture, and indoor air quality. In meteorology, RH is used to predict weather patterns and monitor atmospheric conditions. In agriculture, RH is important for determining the ideal conditions for plant growth and preventing crop damage due to high or low humidity. In indoor air quality, RH is a key factor in maintaining a comfortable and healthy environment for occupants.

5. How can RH be controlled or adjusted in an indoor setting?

RH can be controlled or adjusted in an indoor setting by using devices such as humidifiers and dehumidifiers, which add or remove water vapor from the air, respectively. Additionally, proper ventilation and air conditioning can help regulate RH by bringing in fresh air and removing excess moisture. Monitoring and maintaining a consistent temperature can also help control RH levels.

Similar threads

Replies
10
Views
1K
Replies
9
Views
1K
  • General Math
3
Replies
74
Views
15K
  • STEM Academic Advising
Replies
21
Views
2K
  • Linear and Abstract Algebra
Replies
3
Views
3K
  • Linear and Abstract Algebra
Replies
2
Views
4K
  • STEM Academic Advising
Replies
8
Views
822
  • Science and Math Textbooks
Replies
0
Views
645
  • STEM Academic Advising
Replies
4
Views
1K
Back
Top