Lower bounds for relative class numbers of imaginary abelian number fields and CM-fields
Lower bounds for the conductor of L-functions
Lower bounds of discrete moments of the derivatives of the Riemann zeta-function on the critical line
We establish unconditional lower bounds for certain discrete moments of the Riemann zeta-function and its derivatives on the critical line. We use these discrete moments to give unconditional lower bounds for the continuous moments , where is a non-negative integer and a rational number. In particular, these lower bounds are of the expected order of magnitude for .
Lower order terms for the one-level densities of symmetric power L-functions in the level aspect
Lower order terms in the 1-level density for families of holomorphic cuspidal newforms
Lower order terms of the second moment of S(t)
L-Series, Modular Imbeddings, and Signatures.
Majoration au point 1 des fonctions L associées aux caractères de Dirichlet primitifs, ou au caractère d'une extension quadratique d'un corps quadratique imaginaire principal.
Majoration du nombre de zéros d’une somme polynomiale d’exponentielles -adiques
Mean value estimates for exponential sums and L-functions: a spectral theoretic approach.
Mean value estimates for exponential sums with applications to -functions
Mean Value Properties of the Hurwitz Zeta-Function.
Mean value results for the approximate functional equation of the square of the Riemann zeta-function
Mean value theorems for L-functions over prime polynomials for the rational function field
The first and second moments are established for the family of quadratic Dirichlet L-functions over the rational function field at the central point s=1/2, where the character χ is defined by the Legendre symbol for polynomials over finite fields and runs over all monic irreducible polynomials P of a given odd degree. Asymptotic formulae are derived for fixed finite fields when the degree of P is large. The first moment obtained here is the function field analogue of a result due to Jutila in the...
Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series
We obtain formulas for computing mean values of Dirichlet polynomials that have more terms than the length of the integration range. These formulas allow one to compute the contribution of off-diagonal terms provided one knows the correlation functions for the coefficients of the Dirichlet polynomials. A smooth weight is used to control error terms, and this weight can in typical applications be removed from the final result. Similar results are obtained for the tails of Dirichlet series. Four examples...
Mean values of Hecke L-functions.
Mean values of the Riemann zeta-function and its derivatives.
Mean-periodicity and zeta functions
This paper establishes new bridges between zeta functions in number theory and modern harmonic analysis, namely between the class of complex functions, which contains the zeta functions of arithmetic schemes and closed with respect to product and quotient, and the class of mean-periodic functions in several spaces of functions on the real line. In particular, the meromorphic continuation and functional equation of the zeta function of an arithmetic scheme with its expected analytic shape is shown...
Meromorphic extensions of generalised zeta functions.
Minoration au point 1 des fonctions L et détermination des corps sextiques abéliens totalement imaginaires principaux