- #1

jqmhelios

- 11

- 7

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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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

- 11

- 7

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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- #2

mathwonk

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https://www.abebooks.com/servlet/SearchResults?sts=t&cm_sp=SearchF-_-home-_-Results&tn=lectures on modular forms&an=robert gunning

gunning will not of course include the modern applications to fermat's theorem that are apparently the goal of the GTM book you mention.

- #3

Infrared

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I found the last chapter of Serre's a course in arithemtic very well written and readable.

- #4

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Perhaps you would like to know that modular forms have applications in physics, see e.g. https://arxiv.org/abs/2208.07242jqmhelios 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.

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.

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.

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.

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.

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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