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Shimura curves and the abc conjecture - MaRDI portal

Shimura curves and the abc conjecture (Q6048610)

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scientific article; zbMATH DE number 7748223

Language	Label	Description	Also known as
English	Shimura curves and the abc conjecture	scientific article; zbMATH DE number 7748223

Statements

scholarly article

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Shimura curves and the abc conjecture (English)

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Journal of Number Theory

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publication date

11 October 2023

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full work available at URL

https://arxiv.org/abs/1705.09251

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zbMATH Keywords

Shimura curves

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elliptic curves

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abc conjecture

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MaRDI profile type

MaRDI publication profile

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The Manin constant. (With an appendix by J. Cremona)

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The modular degree, congruence primes, and multiplicity one

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Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)

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Hecke operators on \(\Gamma_0(m)\)

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\(p\)-adic periods, \(p\)-adic \(L\)-functions, and the \(p\)-adic uniformization of Shimura curves.

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Bounding sup-norms of cusp forms of large level

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On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises

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Effective multiplicity one on GL n and narrow zero-free regions for Rankin-Selberg L- functions

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Integral models of certain Shimura curves

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Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert

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A modular description of \(\mathscr X_0(n)\)

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The Manin constant in the semistable case

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The modular degree and the congruence number of a weight 2 cusp form

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Periods of abelian varieties with complex multiplication

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\(p\)-adic \(L\)-functions and the coniveau filtration on Chow groups. With an appendix by Brian Conrad.

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On the Equations <i>z<sup>m</sup> </i> = <i>F</i> (<i>x, y</i> ) and <i>Ax<sup>p</sup> </i> + <i>By<sup>q</sup> </i> = <i>Cz<sup>r</sup> </i>

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\(L^{\infty}\) norms of holomorphic modular forms in the case of compact quotient

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Les Schémas de Modules de Courbes Elliptiques

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Modularity of a family of elliptic curves

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Base change for elliptic curves over real quadratic fields

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COMPARISON OF INTEGRAL STRUCTURES ON SPACES OF MODULAR FORMS OF WEIGHT TWO, AND COMPUTATION OF SPACES OF FORMS MOD 2 OF WEIGHT ONE. WITH APPENDICES BY JEAN-FRANÇOIS MESTRE AND GABOR WIESE

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Finiteness theorems for abelian varieties over number fields.

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L'ensemble exceptionnel dans la conjecture de Szpiro

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Elliptic curves over real quadratic fields are modular

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THE JACQUET–LANGLANDS CORRESPONDENCE AND THE ARITHMETIC RIEMANN–ROCH THEOREM FOR POINTED CURVES

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A large sieve density estimate near \(\sigma = 1\)

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Polarization and isogenies

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Elliptic curves and automorphic representations

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DISTINGUISHING HECKE EIGENFORMS

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Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur

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Local Orders, Root Numbers, and Modular Curves

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Heegner points and derivatives of \(L\)-series

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On the abc conjecture in algebraic number fields

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Courbes de Fermat: résultats et problèmes

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A mean value estimate for real character sums

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On maps between modular Jacobians and Jacobians of Shimura curves

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Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman

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On the Euler-Kronecker constants of global fields and primes with small norms

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On the logarithmic derivatives of Dirichlet L-functions at s=1

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On the Arakelov theory of elliptic curves

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Arithmetic Moduli of Elliptic Curves. (AM-108)

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Integral points on moduli schemes of elliptic curves

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Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture

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On the number of Q-isomorphism classes of elliptic curves in each Q- isogeny class

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Modular Forms and Special Cycles on Shimura Curves. (AM-161)

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The distribution of Euler-Kronecker constants of quadratic fields

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L-series of Rankin type and their functional equations

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A theorem on analytic strong multiplicity one

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Dimensions of the spaces of cusp forms and newforms on \(\Gamma_0(N)\) and \(\Gamma_1(N)\)

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Rational isogenies of prime degree. (With an appendix by D. Goldfeld)

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Courbes de Weil semi-stables de discriminant une puissance m-ième.

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Primary cyclotomic units and a proof of Catalans conjecture

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Modular forms and effective Diophantine approximation

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Majorations Explicites Pour le Nombre de Diviseurs de <i>N</i>

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Optimal Quotients of Jacobians With Toric Reduction and Component Groups

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Integrality of a ratio of Petersson norms and level-lowering congruences

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Remarks on the size of the Tamagawa product

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On the Phragmén-Lindelöf theorem and some applications

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On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms

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On the equation $a^p + 2^α b^p + c^p = 0$

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Parametrizations of elliptic curves by Shimura curves and by classical modular curves

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On zeta functions of quaternion algebras

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Construction of class fields and zeta functions of algebraic curves

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The Arithmetic of Elliptic Curves

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On the Oesterlé-Masser conjecture

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On the \(abc\) conjecture

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On the \(abc\) conjecture. II.

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Effectiveness of Siegel's theorem and the abc conjecture

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Degrees of parametrizations of elliptic curves by Shimura curves

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Ring-theoretic properties of certain Hecke algebras

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Hauteur de Faltings de quotients de J o( N ), discriminants d'algebres de Hecke et congruences entre formes modulaires

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On the Hida constant of modular curves and Shimura curves

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Diophantine approximations and value distribution theory

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Diophantine Approximation and Nevanlinna Theory

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An effective lower bound for the height of algebraic numbers

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The analytic strong multiplicity one theorem for \(\text{GL}_m(\mathbb A_K)\)

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The least prime ideal.

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Modular elliptic curves and Fermat's Last Theorem

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P-adic logarithmic forms and group varieties III

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Modular Parametrizations of Elliptic Curves

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The Gross-Zagier Formula on Shimura Curves

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On the averaged Colmez conjecture

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Heights of Heegner points on Shimura curves.

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Gross-Schoen cycles and dualising sheaves

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Identifiers

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10.1016/j.jnt.2023.07.002

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:6048610

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