Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Accounts of modular forms say that they were studied in the early 19th century, but then define modular forms using terminology that didn't exist until the 20th century. How did the earliest mathematicians to investigate modular forms define them? What motivated their exploration?

share|improve this question

2 Answers 2

up vote 9 down vote accepted

There is also the book of F. Klein, Development of Mathematics in XIX century, vol. I, which has a large chapter on Gauss which describes his work on modular forms. This was written in XX century, but Klein was essentially a XIX century mathematician, so you can see from this book "how did they think".

share|improve this answer

An enjoyable account how Gauss, Abel, and Weierstrass thought (or might have thought) about elliptic integrals and modular forms is given by Dick Koch, The Pentagonal Number Theorem and Modular Forms, pages 13-27.

share|improve this answer
    
Very nice paper of Koch. Thanks. –  Alexandre Eremenko Nov 11 '13 at 20:01

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.