• Corpus ID: 248721980

A Motivic Pairing and the Mellin Transform in Function Fields

@inproceedings{Green2022AMP,
  title={A Motivic Pairing and the Mellin Transform in Function Fields},
  author={Nathan Green},
  year={2022}
}
. We define two pairings relating the A -motive with the dual A -motive of an abelian Anderson A -module. We show that specializations of these pairings give the exponential and logarithm functions of this Anderson A -module, and we use these specializations to give precise formulas for the coefficients of the exponential and logarithm functions. We then use this pairing to express the exponential and logarithm functions as evaluations of certain infinite products. As an application of these ideas… 

References

SHOWING 1-10 OF 26 REFERENCES

Special zeta values using tensor powers of Drinfeld modules

We study tensor powers of rank 1 sign-normalized Drinfeld A-modules, where A is the coordinate ring of an elliptic curve over a finite field. Using the theory of vector valued Anderson generating

Trivial multiple zeta values in Tate algebras

We study trivial multiple zeta values in Tate algebras. These are particular examples of the multiple zeta values in Tate algebras in positive characteristic introduced by the second author. If the

On log-algebraic identities for Anderson t-modules and characteristic p multiple zeta values

Based on the notion of Stark units we present a new approach that obtains refinements of log-algebraic identities for Anderson t-modules. As a consequence we establish a generalization of Chang's

$t$-Motives: Hodge Structures, Transcendence and Other Motivic Aspects

Drinfeld in 1974, in his seminal paper [10], revolutionized the contribution to arithmetic of the area of global function fields. He introduced a function field analog of elliptic curves over number

Values of certain L-series in positive characteristic

We introduce a class of deformations of the values of the Goss zeta function. We prove, with the use of the theory of deformations of vectorial modular forms as well as with other techniques, a

Desingularization of complex multiple zeta-functions

We introduce the method of desingularization of multi-variable multiple zeta-functions (of the generalized Euler-Zagier type), under the motivation of finding a suitable rigorous meaning of the

Taylor coefficients of t-motivic multiple zeta values and explicit formulae

For each positive characteristic multiple zeta value (defined by Thakur in 2004), the first and third authors recently constructed a t-module such that a certain coordinate of a logarithmic vector of

Tensor powers of rank 1 Drinfeld modules and periods

On a conjecture of Furusho over function fields

In the classical theory of multiple zeta values (MZV’s), Furusho proposed a conjecture asserting that the p -adic MZV’s satisfy the same $${\mathbb {Q}}$$ Q -linear relations that their corresponding

Appendix. the Mellin Transform and Related Analytic Techniques

1. The generalized Mellin transformation The Mellin transformation is a basic tool for analyzing the behavior of many important functions in mathematics and mathematical physics, such as the zeta