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- W4385681661 abstract "For the $mathbb{Z}$-lift $X_mathbb{Z}$ of a monoid scheme $X$ of finite type, Deitmar-Koyama-Kurokawa calculated its absolute zeta function by interpolating $#X_mathbb{Z}(mathbb{F}_q)$ for all prime powers $q$ using the Fourier expansion. This absolute zeta function coincides with the absolute zeta function of a certain polynomial. In this article, we characterize the polynomial as a ceiling polynomial of the sequence $left(#X_mathbb{Z}(mathbb{F}_q)right)_q$, which we introduce independently. Extending this idea, we introduce a certain pair of absolute zeta functions of a separated scheme $X$ of finite type over $mathbb{Q}$ by means of a pair of Puiseux polynomials which estimate $#X(mathbb{F}_{p^m})$ for sufficiently large $p$. We call them the ceiling and floor Puiseux polynomials of $X$. In particular, if $X$ is an elliptic curve, then our absolute zeta functions of $X$ do not depend on its isogeny class." @default.
- W4385681661 created "2023-08-09" @default.
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- W4385681661 date "2023-08-06" @default.
- W4385681661 modified "2023-09-26" @default.
- W4385681661 title "Absolute zeta functions arising from ceiling and floor Puiseux polynomials" @default.
- W4385681661 doi "https://doi.org/10.48550/arxiv.2308.03232" @default.
- W4385681661 hasPublicationYear "2023" @default.
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