Displaying similar documents to “Linearly invariant families of holomorphic functions in the unit polydisc”

Explicit lower bounds for linear forms in two logarithms

Nicolas Gouillon (2006)

Journal de Théorie des Nombres de Bordeaux

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We give an explicit lower bound for linear forms in two logarithms. For this we specialize the so-called Schneider method with multiplicity described in []. We substantially improve the numerical constants involved in existing statements for linear forms in two logarithms, obtained from Baker’s method or Schneider’s method with multiplicity. Our constant is around 5 . 10 4 instead of 10 8 .

Special values of symmetric power L -functions and Hecke eigenvalues

Emmanuel Royer, Jie Wu (2007)

Journal de Théorie des Nombres de Bordeaux

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We compute the moments of L -functions of symmetric powers of modular forms at the edge of the critical strip, twisted by the central value of the L -functions of modular forms. We show that, in the case of even powers, it is equivalent to twist by the value at the edge of the critical strip of the symmetric square L -functions. We deduce information on the size of symmetric power L -functions at the edge of the critical strip in subfamilies. In a second part, we study the distribution of...

A constant in pluripotential theory

Zbigniew Błocki (1992)

Annales Polonici Mathematici

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We compute the constant sup ( 1 / d e g P ) ( m a x S l o g | P | - ∫ S l o g | P | d σ ) : P a polynomial in ℂ n , where S denotes the euclidean unit sphere in ℂ n and σ its unitary surface measure.