Modular Forms: A Textbook for University Physics Students

In summary, The conversation is about the topic of modular forms and the request for recommendations on textbooks about it. The person mentions being a physics student and their interest in this subject. They ask for an "accessible" textbook and inquire about the quality of a specific book. The other person recommends a more modern book, but also mentions a well-written and readable older book. They also mention that modular forms have applications in physics.
  • #1
jqmhelios
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I'm studying physics at university, but there has always been one subject in pure maths which always interested me- that is modular forms.
Is there an 'accessible' textbook on this topic? Can anyone recommend one? Is the GTM Springer 'A first course in modular forms' any good?
 
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  • #3
I found the last chapter of Serre's a course in arithemtic very well written and readable.
 
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  • #4
jqmhelios said:
I'm studying physics at university, but there has always been one subject in pure maths which always interested me- that is modular forms.
Perhaps you would like to know that modular forms have applications in physics, see e.g. https://arxiv.org/abs/2208.07242
 
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FAQ: Modular Forms: A Textbook for University Physics Students

What are modular forms?

Modular forms are complex functions that are invariant under a certain group of transformations and satisfy specific conditions. They are a central concept in number theory and have applications in various areas of mathematics and physics, including string theory and the theory of elliptic curves.

How are modular forms relevant to university physics students?

Modular forms are relevant to university physics students because they appear in advanced topics such as quantum field theory, string theory, and statistical mechanics. Understanding modular forms can provide deeper insights into the mathematical structures underlying these physical theories.

What prerequisites are needed to understand modular forms?

To understand modular forms, students typically need a solid background in complex analysis, linear algebra, and abstract algebra. Familiarity with number theory and differential equations can also be beneficial.

Can you provide an example of a modular form?

An example of a modular form is the Eisenstein series, which is a series of functions that are invariant under the action of the modular group. Specifically, the Eisenstein series of weight k is given by the sum over lattice points in the complex plane, excluding the origin.

What are some applications of modular forms in physics?

Modular forms have applications in various areas of physics. For example, they are used in the study of black hole entropy, partition functions in statistical mechanics, and dualities in string theory. They also appear in the context of conformal field theory and the AdS/CFT correspondence.

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