More than 41% of the zeros of the zeta function are on the critical line
More than two fifths of the zeros of the Riemann zeta function are on the critical line.
Motivic Artin -functions and a motivic Tamagawa number. (Fonctions d'Artin et nombre de Tamagawa motiviques.)
Multiple Dirichlet series over rational function fields
Multiple finite Riemann zeta functions
Multiple zeta values and periods of moduli spaces
We prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces of Riemann spheres with marked points are multiple zeta values. We do this by introducing a differential algebra of multiple polylogarithms on and proving that it is closed under the operation of taking primitives. The main idea is to apply a version of Stokes’ formula iteratively to reduce each period integral to multiple zeta values. We also give a geometric interpretation of the double shuffle...
Multiple zeta values for coordinatewise limits at non-positive integers
Multiplicative functions dictated by Artin symbols
Granville and Soundararajan have recently suggested that a general study of multiplicative functions could form the basis of analytic number theory without zeros of L-functions; this is the so-called pretentious view of analytic number theory. Here we study multiplicative functions which arise from the arithmetic of number fields. For each finite Galois extension K/ℚ, we construct a natural class of completely multiplicative functions whose values are dictated by Artin symbols, and we show that...
Multiplicity results for the functional equation of the Dirichlet L-functions: case p=2
Multiplicity results for the functional equation of the Dirichlet L-functions
Multizetas, perinomal numbers, arithmetical dimorphy, and ARI/GARI