Displaying 381 – 400 of 440

Showing per page

Multiple zeta values and periods of moduli spaces 𝔐 ¯ 0 , n

Francis C. S. Brown (2009)

Annales scientifiques de l'École Normale Supérieure

We prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces 𝔐 0 , n of Riemann spheres with n marked points are multiple zeta values. We do this by introducing a differential algebra of multiple polylogarithms on 𝔐 0 , n 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...

Multiplicative Dedekind η -function and representations of finite groups

Galina Valentinovna Voskresenskaya (2005)

Journal de Théorie des Nombres de Bordeaux

In this article we study the problem of finding such finite groups that the modular forms associated with all elements of these groups by means of a certain faithful representation belong to a special class of modular forms (so-called multiplicative η - products). This problem is open.We find metacyclic groups with such property and describe the Sylow p -subgroups, p 2 , for such groups. We also give a review of the results about the connection between multiplicative η -products and elements of finite orders...

Multiplicative dependence of shifted algebraic numbers

Paulius Drungilas, Artūras Dubickas (2003)

Colloquium Mathematicae

We show that the set obtained by adding all sufficiently large integers to a fixed quadratic algebraic number is multiplicatively dependent. So also is the set obtained by adding rational numbers to a fixed cubic algebraic number. Similar questions for algebraic numbers of higher degrees are also raised. These are related to the Prouhet-Tarry-Escott type problems and can be applied to the zero-distribution and universality of some zeta-functions.

Currently displaying 381 – 400 of 440