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- W2495100098 abstract "The period polynomial $r_f(z)$ for a weight $k geq 3$ newform $f in S_k(Gamma_0(N),chi)$ is the generating function for special values of $L(s,f)$. The functional equation for $L(s, f)$ induces a functional equation on $r_f(z)$. Jin, Ma, Ono, and Soundararajan proved that for all newforms $f$ of even weight $k ge 4$ and trivial nebetypus, the Riemann Hypothesis holds for $r_f(z)$: that is, all roots of $r_f(z)$ lie on the circle of symmetry $|z| =1/sqrt{N}$. We generalize their methods to prove that this phenomenon holds for all but possibly finitely many newforms $f$ of weight $k ge 3$ with any nebentypus. We also show that the roots of $r_f(z)$ are equidistributed if $N$ or $k$ is sufficiently large." @default.
- W2495100098 created "2016-08-23" @default.
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- W2495100098 date "2016-07-16" @default.
- W2495100098 modified "2023-09-27" @default.
- W2495100098 title "The Riemann Hypothesis is True for Period Polynomials of Almost All Newforms" @default.
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