I am a sophomore and have the foundation of complex analysis and abstract algebra. I have learned Legendre elliptic integral and Jacobian elliptic function, and it is through this that I know theta function. Recently, I was reading Mumford's Tata collections on theta, but I got stuck in the module form of Volume I, and I felt that I had touched a new field. Do you need any pre knowledge before reading "Tata"? I just want to finish reading the three volumes smoothly, and maybe I don't want to touch the irrelevant contents outside the three volumes for the time being.
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1$\begingroup$ At least for later sections, some knowledge of complex algebraic geometry would be helpful. $\endgroup$– Donu ArapuraCommented Dec 26, 2022 at 20:34
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$\begingroup$ I have only read chapter 2 of volume 1, but I do not recall any specialized knowledge needed, beyond what you have. I believe you also can read that chapter, and I recommend it highly. Forgive me, but in general I believe the only way to find out if you are prepared to read something is to try, and even then, to persist. good luck! $\endgroup$– roy smithCommented Dec 27, 2022 at 4:40
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$\begingroup$ Thank you for your answer,Donu Arapura. It seems to be a difficult road, but I will try my best! $\endgroup$– ZoeCommented Dec 27, 2022 at 13:17
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$\begingroup$ Thank you for your answer,Roy Smith. I am so excited! To tell you the truth, I seem to see your name at the beginning of Chapter 2. You write the exponential part of the expansion of theta function as the sum of quadratic function and linear function,unbelievable! I would like to ask, is there any inheritance between Chapter 2 and Chapter 1? Because it seems that you only read the second chapter 2. Didn't you read the first chapter? $\endgroup$– ZoeCommented Dec 27, 2022 at 13:19
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