Power Series Expansion of Dedekind Eta Function: How to Expand η(τ)/η(3τ)?

Click For Summary
SUMMARY

The discussion focuses on computing the power series expansion of the Dedekind eta function, specifically η(τ)/η(3τ). The eta function is defined as η(τ) = q^24 ∏(1 - q^n) for n from 0 to infinity, where q = e^(2πiτ). The user seeks assistance in expanding this function while working on the modular polynomial related to the prime number 3. Clarification is also requested regarding whether the eta function is equivalent to the alternating zeta function.

PREREQUISITES
  • Understanding of modular forms and functions
  • Familiarity with the Dedekind eta function
  • Knowledge of power series expansions
  • Basic concepts of complex analysis, particularly in relation to q-series
NEXT STEPS
  • Research the properties of the Dedekind eta function and its applications in number theory
  • Learn about modular polynomials and their significance in modular forms
  • Study the relationship between the eta function and the alternating zeta function
  • Explore techniques for computing power series expansions in complex analysis
USEFUL FOR

Mathematicians, number theorists, and students studying modular forms or complex analysis who are interested in the properties and applications of the Dedekind eta function.

twoforone
Messages
3
Reaction score
0
Hi Every body!

I wan to compute the power series expansion of dedekind eta function. Specifically, I want to know the power series expansion of η(τ)/η(3τ)? How could I expand this function? I would be happy if you could help me as I am stuck at this state when I am computing the modular polynomial of prime number 3.
 
Physics news on Phys.org
is eta the alternating zeta function??
 
eta function is a function with this expression
infinity
η(τ)=q^24 ∏(1-q^n)
n=0
where q=e^2πiτ
Sorry, the product is from n=0 up-to infinity. You should understand in that way.
 

Similar threads

Power Series expansion of an eigenvalue
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad On (real) entire functions and the identity theorem
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad How to manipulate functions that are not explicitly given?
  • · Replies 16 ·
Replies
16
Views
3K
How to Expand Noncommuting Variables in a Formal Power Series?
  • · Replies 4 ·
Replies
4
Views
2K
Using Power Series to Evaluate ln and sin at a Given Point
  • · Replies 5 ·
Replies
5
Views
2K
Graduate How Do You Expand Power Series for Complex Functions?
  • · Replies 5 ·
Replies
5
Views
5K
Graduate Expanding in powers of 1/z (Laurent series)
  • · Replies 2 ·
Replies
2
Views
10K
Series expansion of function of two variables
  • · Replies 2 ·
Replies
2
Views
2K
Graduate A question regarding the Power series method of solving the QHO
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Can there be multiple power series representations for a function?
  • · Replies 1 ·
Replies
1
Views
3K