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- W4381551221 abstract "Ramanujan's notebooks contain many elegant identities and one of the celebrated identities is a formula for $zeta(2k+1)$. In 1972, Grosswald gave an extension of the Ramanujan's formula for $zeta(2k+1)$, which contains a polynomial of degree $2k+2$. This polynomial is now well-known as the Ramanujan polynomial$R_{2k+1}(z)$, first studied by Gun, Murty, and Rath. Around the same time, Murty, Smith and Wang proved that all the non-real zeros of $R_{2k+1}(z)$ lie on the unit circle. Recently, Chourasiya, Jamal, and the first author found a new polynomial while obtaining a Ramanujan-type formula for Dirichlet $L$-functions and named it as Ramanujan-type polynomial $R_{2k+1,p}(z)$. In the same paper, they conjectured that all the non-real zeros of $R_{2k+1,p}(z)$ lie on the circle $|z|=1/p$. The main goal of this paper is to present a proof of this conjecture." @default.
- W4381551221 created "2023-06-22" @default.
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- W4381551221 date "2023-06-17" @default.
- W4381551221 modified "2023-10-18" @default.
- W4381551221 title "Zeros of Ramanujan-type Polynomials" @default.
- W4381551221 doi "https://doi.org/10.48550/arxiv.2306.10283" @default.
- W4381551221 hasPublicationYear "2023" @default.
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