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This paper has been withdrawn, as it is superseded by arXiv:0806.2122 (Bloch-Kato exponential maps for local fields with imperfect residue fields), which is a more recent version of the same paper.
We prove that the central values of additive twists of a cuspidal $L$-function define a quantum modular form in the sense of Zagier, generalizing recent results of Bettin and Drappeau. From this we deduce a reciprocity law for the twisted first momen
Let $M_{d,n}(q)$ denote the number of monic irreducible polynomials in $mathbb{F}_q[x_1, x_2, ldots , x_n]$ of degree $d$. We show that for a fixed degree $d$, the sequence $M_{d,n}(q)$ converges $q$-adically to an explicitly determined rational func
The paper contained a preliminary version of a general theory of reciprocity laws on vector spaces.
By virtue of Baileys well-known bilateral 6psi_6 summation formula and Watsons transformation formula,we extend the four-variable generalization of Ramanujans reciprocity theorem due to Andrews to a five-variable one. Some relevant new q-series ident
Assuming Schanuels conjecture, we prove that any polynomial exponential equation in one variable must have a solution that is transcendental over a given finitely generated field. With the help of some recent results in Diophantine geometry, we obtai