The Gross–Zagier–Zhang formula over function fields
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DOI: 10.1007/s00208-021-02289-1
Abstract: We prove the Gross-Zagier-Zhang formula over global function fields of arbitrary characteristics. It is an explicit formula which relates the Neron-Tate heights of CM points on abelian varieties and central derivatives of associated quadratic base… read more here.
Keywords: formula; zhang; gross zagier; function fields ... See more keywords
Arithmetic degrees for dynamical systems over function fields of characteristic zero
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DOI: 10.1007/s00209-018-2053-x
Abstract: We study the arithmetic degree of a dominant rational self-map on a smooth projective variety over a function field of characteristic zero. We interpret the notion of arithmetic degree and study related problems over function… read more here.
Keywords: arithmetic degree; arithmetic degrees; characteristic zero; degree ... See more keywords
Ramanujan graphs and exponential sums over function fields
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DOI: 10.1016/j.jnt.2020.05.010
Abstract: We prove that $q+1$-regular Morgenstern Ramanujan graphs $X^{q,g}$ (depending on $g\in\mathbb{F}_q[t]$) have diameter at most $\left(\frac{4}{3}+\varepsilon\right)\log_{q}|X^{q,g}|+O_{\varepsilon}(1)$ (at least for odd $q$ and irreducible $g$) provided that a twisted Linnik-Selberg conjecture over $\mathbb{F}_q(t)$ is true. This… read more here.
Keywords: sums function; ramanujan graphs; graphs exponential; exponential sums ... See more keywords
Logarithmic-type and exponential-type hypergeometric functions for function fields
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DOI: 10.1016/j.jnt.2021.05.016
Abstract: Abstract This article suggests a new hypergeometric function for function fields and a new operator such that the Drinfeld logarithm is stable under it, and studies an equation satisfied by the hypergeometric function. As applications,… read more here.
Keywords: type exponential; logarithmic type; exponential type; function fields ... See more keywords
ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS
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DOI: 10.1017/s0004972720001094
Abstract: Abstract Let $ (G_n)_{n=0}^{\infty } $ be a nondegenerate linear recurrence sequence whose power sum representation is given by $ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $ . We prove… read more here.
Keywords: growth linear; function fields; recurrences function; linear recurrences ... See more keywords
Construction of Sequences With High Nonlinear Complexity From Function Fields
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DOI: 10.1109/tit.2017.2736545
Abstract: Complexity of sequences plays an important role in pseudorandom sequences and cryptography. In this paper, we present a construction of sequences with high nonlinear complexity from function fields. The main idea is to make use… read more here.
Keywords: nonlinear complexity; construction sequences; complexity; function fields ... See more keywords
Constructions of Locally Repairable Codes With Multiple Recovering Sets via Rational Function Fields
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DOI: 10.1109/tit.2019.2946627
Abstract: Locally repairable codes with more than one recovering set are demanded in the application to distributed storage. For each failure node (or disk), it is desired to have as many recovering sets as possible. In… read more here.
Keywords: recovering sets; multiple recovering; locally repairable; function fields ... See more keywords
Cubic function fields with prescribed ramification
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DOI: 10.1142/s1793042121500755
Abstract: This paper describes cubic function fields [Formula: see text] with prescribed ramification, where [Formula: see text] is a rational function field. We give general equations for such extensions, an explicit procedure to obtain a defining… read more here.
Keywords: prescribed ramification; function fields; formula see; see text ... See more keywords