Smyth, Christopher

Edinburgh Research Explorer

English

A generalization of a theorem of Schinzel,

A lower bound for linear forms in logarithms,

A lower bound for the canonical height on abelian varieties over abelian extensions,

A lower bound for the canonical height on elliptic curves over abelian extensions,

A lower bound for the height in abelian extensions,

A note on heights in certain in extensions of Q,

A note on integer symmetric matrices and Mahler's measure,

A q-Mahler measure,

A re of two theorems of Kronecker,

A relative Dobrowolski lower bound over abelian extensions,

A remark on a paper of mine on polynomials,

A remarkable class of algebraic integers. Proof of a conjecture of Vijayaraghavan,

Algebraic integers near the unit circle,

Algebraic integers on the unit circle,

Algebraic integers whose conjugates lie in the unit circle,

Algebraic integers whose conjugates lie near the unit circle,

Algebraic number theory,

Algebraic numbers close to 1 and variants of Mahler's measure,

Algebraic numbers close to both 0 and 1,

Algebraic numbers near the unit circle,

Algebraic points on subvarieties of Gn m.

An areal analog of Mahler's measure,

An eective lower bound for the height of algebraic numbers,

An inequality for the discriminant of a polynomial,

Analytic theory of polynomials, London Mathematical Society Monographs. New Series 26. The Clarendon Press,

and Salem numbers in intervals of the real line,

Approximation des nombres alg ebriques par des nombres alg ebriques de grand degr e,

arithmetic and geometric properties of Mahler measures,

Bounding the elliptic Mahler measure,

Calculs explicites de constantes de Lehmer, Groupe de travail en th eorie analytique et

Computational excursions in analysis and number theory,

concerning the range of Mahler's measure,

Conjecture de Lehmer et petits nombres de Salem, Queen's Papers

Counting points of small height on elliptic curves,

Cyclotomic partitions, Number theory (Ban,

de combinaisons lin eaires de logarithmes de nombres alg ebriques,

die im Innern des Einheitskreises beschr ankt sind. I, II,

Diophantine approximation on linear algebraic groups. Transcendence properties of the exponential function in several variables,

Distribution des points de petite hauteur dans les groupes multiplicatifs.

egalit es sur la mesure de Mahler d'un polyn^ ome,

Entiers alg ebriques dont les conjugu es sont proches du cercle unit e, S eminaire Delange-Pisot-Poitou, 19e ann ee: 1977/78, Th eorie des nombres,

Ergodic automorphisms of the in torus are Bernoulli,

Factorization of certain cyclotomic functions,

Fields with large Kronecker constants,

Gon calves,

Heights in Diophantine geometry,

heights of perturbed polynomials, 21st Journ ees Arithm etiques (Rome,

Heights of points on subvarieties of Gn m, Number theory (Paris,

Heights of polynomials and entropy in algebraic dynamics, Universitext. Springer-Verlag London Ltd.,

Heights, Graduate lecture course,

Integer symmetric matrices of small index and small Mahler measure,

Knot theory, Transl. from the German and ed. by Leo

Le probl eme de Lehmer en dimension sup erieure.

Le probl eme de Lehmer: m ethode de Dobrowolski et lemme de Siegel \ a la Bombieri-Vaaler&quot;,

le produit des conjugu es ext erieurs au cercle unit e d'un entier alg ebrique,

Le th eor eme de Dobrowolski en dimension sup erieure,

Lehmer's problem for polynomials with odd coecients,

les nombres alg ebriques de petite mesure, Mathematics,

Lower bounds for heights on elliptic curves,

Lower bounds for the canonical height on elliptic curves over abelian extensions,

Lower bounds of heights of points on hypersurfaces,

Lower bounds on the projective heights of algebraic points,

Mahler measure of Alexander polynomials,

Mahler measure, links and homology growth,

Mahler's measure and the dilogarithm.

Mahler's measure, Paci Institute for the

measure and invariants of hyperbolic manifolds, Number theory for the millennium,

measure and special values of L-functions,

measure of a polynomial in function of the number of its coecients,

measure of a polynomial in terms of the number of its monomials,

measure: from number theory to geometry, this volume,

measures close to an integer,

measures generate the largest possible groups,

Measuring the height of a polynomial,

Minoration d'un produit pond er e des conjugu es d'un entier alg ebrique totalement r

Minoration de la hauteur de N eron-Tate, Seminar on number theory,

Minoration de la hauteur normalis ee dans un tore.

Minoration de la hauteur normalis ee des hypersurfaces.

Minorations pour les mesures de Mahler de certains polyn^ omes particuliers,

Modular Mahler measures. I, Topics in number theory

Multiplicative relations in number

Nombres alg ebriques de petite mesure et formes lin eaires en un logarithme,

Nombres transcendants et groupes alg ebriques, Ast erisque 69{70.

Nonreciprocal algebraic numbers of small measure,

numbers which are Mahler measures,

On a conjecture of A. Schinzel

On a conjecture of D.H.

On a connection between the Mahler measure and the discriminant of algebraic numbers,

On a limiting fractal measure de by conjugate algebraic integers,

On a problem of Lehmer, Studies in pure mathematics, 135{144, Birkh auser,

On a problem of Schinzel and Zassenhaus.

On a question of Lehmer and the number of irreducible factors of a polynomial,

On a question of Lehmer. Abelian functions and transcendental numbers (Colloq.,  Ecole Polytech.,

on a theme of Kronecker,

On a theorem of Dobrowolski about the product of conjugate numbers,

On a theorem of Kronecker and a related question of Lehmer,

On algebraic numbers close to 1,

On algebraic numbers of small height: linear forms in one logarithm,

On algebraic numbers of small measure,

On an inequality of J. Vicente Gon calves, Univ. Lisboa Revista Fac.

Mahler measure of one-variable polynomials: a survey.

The theory of Modular Forms has been central in mathematics with a
  rich history and connections to many other areas of mathematics. The   
  workshop explored recent developments and future directions with a  
  particular focus on connections to the theory of periods

Repositorium für Naturwissenschaften und Technik

Modular Forms

The aim of this Arbeitsgemeinschaft is to go over the proof of the higher Gross–Zagier formula established in the paper [YZ15]. The formula relates arbitrary order central derivative of the base change $L$-function of an unramifed automorphic representation of PGL$_2$ over a function field to the self-intersection number of a certain algebraic cycle on the moduli stack of Shtukas

Arbeitsgemeinschaft: Higher Gross Zagier Formulas

Let $B$ be a simple CM abelian variety over a CM field $E$, $p$ a rational
prime. Suppose that $B$ has potentially ordinary reduction above $p$ and is
self-dual with root number $-1$. Under some further conditions, we prove the
generic non-vanishing of (cyclotomic) $p$-adic heights on $B$ along
anticyclotomic $\Z_{p}$-extensions of $E$. This provides evidence towards
Schneider's conjecture on the non-vanishing of $p$-adic heights. For CM
elliptic curves over $\Q$, the result was previously known as a consequence of
work of Bertrand, Gross--Zagier and Rohrlich in the 1980s. Our proof is based
on non-vanishing results for Katz $p$-adic $L$-functions and a Gross--Zagier
formula relating the latter to families of rational points on $B$.Comment: Ann. Inst. Fourier, to appea

Burungale, Ashay

Disegni, Daniel

arXiv.org e-Print Archive

Numérisation de Documents Anciens Mathématiques

Annales de l’institut Fourier (AIF)

Caltech Authors

On the non-vanishing of $p$-adic heights on CM abelian varieties, and
  the arithmetic of Katz $p$-adic $L$-functions