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Questions about modular forms and related areas

5 votes

Verifying coefficients of modular forms

I think Ramsey's answer hits the important points, but I wanted to comment on the converse theorem. The converse theorem takes as an input a Dirichlet series (more generally, an $L$-function) whose a …
B R's user avatar
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6 votes
Accepted

Adjoint of Atkin-Lehner's U_p

The following is essentially taken from Miyake's "On Automorphic Forms on GL2 and Hecke Operators", with some help interpreting notation by looking at Gelbart's "Automorphic forms on adele groups". F …
B R's user avatar
  • 3,183
4 votes

Are the $L$-functions of $X_0(N)$ automorphic?

The zeta function of the modular curve $X_0(N)$ is the product of the $L$-functions of a basis of cusp forms of weight 2 for $\Gamma_0(N)$ (the basis taken to be normalized eigenforms for the Hecke op …
B R's user avatar
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8 votes

Narratives in modular curves

I'll be straying outside of my expertise here, so the following probably contains some errors. I'm just adding my perspective as someone who has (at one time at least) thought about some of this stuff …
14 votes

Modular forms and the Riemann Hypothesis

I know two statements about modular forms that are Riemann Hypothesis-ish. First, note that the constant term of the level-one non-holomorphic Eisenstein series $E_s$ is $y^s+c(s)y^{-s}$, and that t …
B R's user avatar
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