I am self studying Analytic number theory from Apostol Dirichlet series and modular functions in number theory and I have a doubt regarding defintions of modular forms and modular functions. My question is - Both in definitions of Modular functions and entire Modular forms, the function f is assumed to be meromorphic and analytic in upper half plane H respectively . Is there any specific reason that functions are assumed to behave particular in upper half plane H not any other region of complex plane? Why only upper half plane H is chosen not any other region?
2026-03-25 04:36:50.1774413410
Regarding definitions of modular functions and modular forms
299 Views Asked by user775699 https://math.techqa.club/user/user775699/detail AtRelated Questions in ANALYTIC-NUMBER-THEORY
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