scholarly journals Multiple polylogarithms, polygons, trees and algebraic cycles

2009 ◽  
pp. 547-593 ◽  
Author(s):  
H. Gangl ◽  
A. B. Goncharov ◽  
A. Levin
Keyword(s):  
Algebraic Cycles ◽  
Multiple Polylogarithms

Lectures on Algebraic Cycles

2009 ◽  
Author(s):  
Spencer Bloch
Keyword(s):  
Algebraic Cycles

An Elementary Proof of Suslin Reciprocity

2005 ◽  
Vol 48 (2) ◽  
pp. 221-236 ◽  
Author(s):  
Matt Kerr
Keyword(s):  
Elementary Proof ◽  
Function Fields ◽  
Algebraic Cycles ◽  
Important Special Case ◽  
Special Case

AbstractWe state and prove an important special case of Suslin reciprocity that has found significant use in the study of algebraic cycles. An introductory account is provided of the regulator and norm maps on Milnor K2-groups (for function fields) employed in the proof.

scholarly journals Clean Single-Valued Polylogarithms

2021 ◽  
Author(s):  
Steven Charlton ◽  
◽  
Claude Duhr ◽  
Herbert Gangl ◽  
◽  
...  
Keyword(s):  
Weight Functions ◽  
Explicit Formulas ◽  
Basic Properties ◽  
Lower Weight ◽  
Functional Relations ◽  
Multiple Polylogarithms ◽  
Real Analytic

We define a variant of real-analytic polylogarithms that are single-valued and that satisfy ''clean'' functional relations that do not involve any products of lower weight functions. We discuss the basic properties of these functions and, for depths one and two, we present some explicit formulas and results. We also give explicit formulas for the single-valued and clean single-valued version attached to the Nielsen polylogarithms Sn,2(x), and we show how the clean single-valued functions give new evaluations of multiple polylogarithms at certain algebraic points.

scholarly journals Symbolic integration and multiple polylogarithms

2013 ◽  
Author(s):  
Christian Bogner ◽  
Francis Brown
Keyword(s):  
Symbolic Integration ◽  
Multiple Polylogarithms

scholarly journals Generalized multiple Dirichlet series and generalized multiple polylogarithms

2006 ◽  
Vol 124 (2) ◽  
pp. 139-158 ◽  
Author(s):  
Kohji Matsumoto ◽  
Hirofumi Tsumura
Keyword(s):  
Dirichlet Series ◽  
Multiple Polylogarithms ◽  
Multiple Dirichlet Series
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