Ranks of rational points of the Jacobian varieties of hyperelliptic curves
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DOI: 10.1016/j.jnt.2018.08.002
Abstract: Abstract In this paper, we obtain bounds for the Mordell–Weil ranks over certain Z p -extensions (including cyclotomic Z p -extensions) of a wide range of abelian varieties defined over a number field F whose… read more here.
Keywords: hyperelliptic curves; points jacobian; jacobian varieties; rational points ... See more keywords
Rational Points on Solvable Curves over ℚ via Non-Abelian Chabauty
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DOI: 10.1093/imrn/rnab141
Abstract: We study the Selmer varieties of smooth projective curves of genus at least two defined over $\mathbb{Q}$ which geometrically dominate a curve with CM Jacobian. We extend a result of Coates and Kim to show… read more here.
Keywords: solvable curves; abelian chabauty; rational points; non abelian ... See more keywords
RATIONAL POINTS ON THE INNER PRODUCT CONE VIA THE HYPERBOLA METHOD
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DOI: 10.1112/s0025579317000183
Abstract: A strong quantitative form of Manin's conjecture is established for a certain variety in biprojective space. The singular integral in an application of the circle method involves the third power of the integral sine function,… read more here.
Keywords: cone via; via hyperbola; inner product; points inner ... See more keywords
Weil polynomials of abelian varieties over finite fields with many rational points
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DOI: 10.1142/s1793042122500804
Abstract: We consider the finite set of isogeny classes of [Formula: see text]-dimensional abelian varieties defined over the finite field [Formula: see text] with endomorphism algebra being a field. We prove that the class within this… read more here.
Keywords: prove class; weil polynomials; see text; rational points ... See more keywords
Rational Points over Finite Fields on a Family of Higher Genus Curves and Hypergeometric Functions
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DOI: 10.11650/tjm.21.2017.7724
Abstract: In this paper we investigate the relation between the number of rational points over a finite field $\mathbb{F}_{p^n}$ on a family of higher genus curves and their periods in terms of hypergeometric functions. For the… read more here.
Keywords: hypergeometric functions; genus curves; points finite; family higher ... See more keywords
On the number of rational points of certain algebraic varieties over finite fields
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DOI: 10.1515/forum-2022-0324
Abstract: Abstract Let 𝔽 q {\mathbb{F}_{q}} be the finite field of odd characteristic p with q elements ( q = p n {q=p^{n}} , n ∈ ℕ {n\in\mathbb{N}} ) and let 𝔽 q * {\mathbb{F}_{q}^{*}} represent… read more here.
Keywords: number rational; rational points; number; finite fields ... See more keywords