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
Minoration au point des fonctions L attachées à des caractères de Dirichlet
Il est connu (voir [1], [3]) que lorsque χ varie parmi les caractères de Dirichlet non quadratiques, nous avons . Nous montrons ici qu’en se restreignant aux caractères d’ordre impair donné, nous avons . Il serait évidemment bien plus satisfaisant de parvenir à prouver un tel résultat sans restreindre χ à varier parmi des caractères d’ordre fixé. Pour les caractères d’ordre pair, nous ne pouvons établir un tel résultat qu’en nous restreignant aux caractères pour lesquels les conducteurs de restent...
Mittelwerte von Hecke Polynomen.
Möbius convolutions and the Riemann hypothesis.
Mod structure of alternating and non-alternating multiple harmonic sums
The well-known Wolstenholme’s Theorem says that for every prime the -st partial sum of the harmonic series is congruent to modulo . If one replaces the harmonic series by for even, then the modulus has to be changed from to just . One may consider generalizations of this to multiple harmonic sums (MHS) and alternating multiple harmonic sums (AMHS) which are partial sums of multiple zeta value series and the alternating Euler sums, respectively. A lot of results along this direction...
Modular case of Levinson's theorem
We evaluate the integral mollified second moment of L-functions of primitive cusp forms and we obtain, for such L-functions, an explicit positive proportion of zeros which lie on the critical line.
Moments of characteristic polynomials enumerate two-rowed lexicographic arrays.
More precise Pair Correlation Conjecture on the zeros of the Riemann zeta function