Displaying similar documents to “Alexander's capacity for intersections of ellipsoids in ℂ N .”

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...

Sign changes of error terms related to arithmetical functions

Paulo J. Almeida (2007)

Journal de Théorie des Nombres de Bordeaux

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Let H ( x ) = ∑ n ≤ x φ ( n ) n - 6 π 2 x . Motivated by a conjecture of Erdös, Lau developed a new method and proved that # { n ≤ T : H ( n ) H ( n + 1 ) < 0 } ≫ T . We consider arithmetical functions f ( n ) = ∑ d ∣ n b d d whose summation can be expressed as ∑ n ≤ x f ( n ) = α x + P ( log ( x ) ) + E ( x ) , where P ( x ) is a polynomial, E ( x ) = - ∑ n ≤ y ( x ) b n n ψ x n + o ( 1 ) and ψ ( x ) = x - ⌊ x ⌋ - 1 / 2 . We generalize Lau’s method and prove results about the number of sign changes for these error terms.

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.