共查询到20条相似文献,搜索用时 0 毫秒
1.
Iva Kodrnja 《The Ramanujan Journal》2018,46(2):509-524
In this paper, we find projective plane models of the modular curves \(X_0(N)\) by constructing maps from \(X_0(N)\) to the projective plane using modular forms. We use eta-quotients of weight 12. We find those eta-quotients in \(M_{12}(\varGamma _0(N))\) which have maximal order of vanishing at infinity. 相似文献
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Walter R Parry 《Journal of Number Theory》1981,13(3):299-302
It is proven that the cusps are the only points which are rational over Q on X0(N) for N = 53, 113 and 137. 相似文献
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The Ramanujan Journal - The goal of the present paper is to show that all the zeros of the Eisenstein series for $$\Gamma _0^*(5)$$ and $$\Gamma _0^*(7)$$ on the standard fundamental domain lie on... 相似文献
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The Ramanujan Journal - This paper is a continuation of our previous works where we study maps from $$X_0(N)$$ , $$N\ge 1$$ , into $${\mathbb {P}}^2$$ constructed via modular forms of the same... 相似文献
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The Ramanujan Journal - We calculate the dimensions of the spaces of invariant vectors under the Klingen congruence subgroup of level $${\mathfrak {p}}^2$$ for all irreducible, admissible... 相似文献
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Let F(X,Y) be an absolutely irreducible polynomial in
such that the algebraic curve C: F(X,Y) = 0 has infinitely many integer points. In this paper we obtain an explicit estimate on the distribution of integer points of C. 相似文献
7.
Florian Breuer 《Transactions of the American Mathematical Society》2007,359(3):1351-1374
Let be a product of Drinfeld modular curves over a general base ring of odd characteristic. We classify those subvarieties of which contain a Zariski-dense subset of CM points. This is an analogue of the André-Oort conjecture. As an application, we construct non-trivial families of higher Heegner points on modular elliptic curves over global function fields.
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Everest Graham; Reynolds Jonathan; Stevens Shaun 《Bulletin London Mathematical Society》2007,39(5):762-770
Let x(P) = AP/B2P denote the x-coordinate of the rational pointP on an elliptic curve in Weierstrass form. We consider whenBP can be a perfect power or a prime. Using Faltings' theorem,we show that for a fixed f > 1, there are only finitely manyrational points P with BP equal to an fth power. Where descentvia an isogeny is possible, we show that there are only finitelymany rational points P with BP equal to a prime, that thesepoints are bounded in number in an explicit fashion, and thatthey are effectively computable. Finally, we prove a strongerversion of this result for curves in homogeneous form. 相似文献
10.
Ethan Cotterill Lia Feital Renato Vidal Martins 《Journal of Pure and Applied Algebra》2018,222(11):3448-3469
In this article we study rational curves with a unique unibranch genus-g singularity, which is of κ-hyperelliptic type in the sense of [27]; we focus on the cases and , in which the semigroup associated to the singularity is of (sub)maximal weight. We obtain a partial classification of these curves according to the linear series they support, the scrolls on which they lie, and their gonality. 相似文献
11.
We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. 相似文献
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《Quaestiones Mathematicae》2013,36(4):513-525
We consider elliptic curves without complex multiplication defined over the rationals or with complex multiplication defined over the Hilbert class field of the endomorphism ring. We examine the distribution of almost prime group orders of these curves when reduced modulo a prime ideal. 相似文献
15.
Linda Lawton 《Archive for Mathematical Logic》2018,57(3-4):429-451
An AE-sentence is a sentence in prenex normal form with all universal quantifiers preceding all existential quantifiers, and the AE-theory of a structure is the set of all AE-sentences true in the structure. We show that the AE-theory of \((\mathscr {L}({\varPi }_1^0), \cap , \cup , 0, 1)\) is decidable by giving a procedure which, for any AE-sentence in the language, determines the truth or falsity of the sentence in our structure. 相似文献
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In this work we determine the group of modular automorphisms of the
Drinfeld modular curve
for any nonconstant polynomial
.Received: 19 September 2002 相似文献
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F. V. Petrov 《Journal of Mathematical Sciences》2007,147(6):7218-7226
Let Γ ⊂ ℝd be a bounded strictly convex surface. We prove that the number kn(Γ) of points of Γ that lie on the lattice
satisfies the following estimates: lim inf kn(Γ)/nd−2 < ∞ for d ≥ 3 and lim inf kn(Γ)/log n < ∞ for d = 2. Bibliography: 9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 344, 2007, pp. 174–189. 相似文献
20.
David B. Jaffe 《Mathematische Annalen》1992,294(1):645-660
Partially supported by a fellowship from the University of Nebraska Research Council 相似文献