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ETH LibraryTaylor Expansions of Modular Forms at CM Points Student Paper Author(s): Rueger, Ryan Publication date: 202311 Permanent link: https://doi.org/10.3929/ethzb000646162 Rights / license: In
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How to fill out taylor expansions of modular

01
Identify the function you want to expand around a particular point.
02
Determine whether the function is differentiable at the point of expansion.
03
Calculate the value of the function at the point of expansion (f(a)).
04
Compute the derivatives of the function up to the desired order at that point (f'(a), f''(a), etc.).
05
Use the Taylor series formula: f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + ... + f^n(a)(x-a)^n/n!
06
Make sure to consider the modular nature of the function when calculating derivatives and values.
07
If applicable, reduce the coefficients modulo the integer relevant to the modular function being used.

Who needs taylor expansions of modular?

01
Mathematicians and researchers working in number theory.
02
Engineers and scientists applying modular arithmetic in their models.
03
Students studying calculus or advanced mathematics.
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Computer scientists focusing on cryptography and algorithm development.
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Taylor expansions of modular are mathematical series that approximate a function using polynomials, typically used to express modular forms in number theory.
Individuals or entities involved in mathematical research or applications related to modular forms typically need to file Taylor expansions of modular.
To fill out Taylor expansions of modular, one must expand a modular function around a specific point using derivatives at that point.
The purpose of Taylor expansions of modular is to simplify complex functions and make them easier to analyze or compute by approximating them with polynomial expressions.
Information that must be reported includes the coefficients of the series, the order of the expansion, and the function being approximated.
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