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For each positive characteristic multiple zeta value defined by Thakur, the first and third authors constructed a t-module such that a certain coordinate of a logarithmic vector of a specified algebraic point is a rational multiple of that multiple zeta value. The main result in this paper gives explicit formulae for all of the coordinates of this logarithmic vector in terms of Taylor coefficients of t-motivic multiple zeta values and t-motivic Carlitz multiple star polylogarithms.

We study the structures of Fourier coefficients of automorphic forms on symplectic groups based on their local and global structures related to Arthur parameters. This is a first step towards the general conjecture on the relation between the structure of Fourier coefficients and Arthur parameters for automorphic forms occurring in the discrete spectrum, given by the first named author.

The endoscopic classification via the stable trace formula comparison provides certain character relations between irreducible cuspidal automorphic representations of classical groups and their global Arthur parameters, which are certain automorphic representations of general linear groups. It is a question of J. Arthur and W. Schmid that asks how to construct concrete modules for irreducible cuspidal automorphic representations of classical groups in term of their global Arthur parameters? In this paper, we formulate a general construction of concrete modules, using Bessel periods, for cuspidal automorphic representations of classical groups with generic global Arthur parameters. Then we establish the theory for orthogonal and unitary groups, based on certain well expected conjectures. Among the consequences of the theory in this paper is that the global Gan-Gross-Prasad conjecture for those classical groups is proved in full generality in one direction and with a global assumption in the other direction.