On Pellarin’s $L$-series

Perkins, Rudolph

doi:10.1090/s0002-9939-2014-12080-6

Cited by 14 publications

(25 citation statements)

References 13 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The formula. The next Theorem directly follows from Theorem 11.3, proved in the appendix by Florent Demeslay, by means of Proposition 5.9 and the isomorphism (16).…”

Section: 3mentioning

confidence: 84%

Arithmetic of positive characteristic -series values in Tate algebras

Pellarin²,

et al. 2015

View full text Add to dashboard Cite

With an appendix by F. Demeslay 2 .Abstract. The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the values at one of these L-series encode arithmetic information of a generalization of Drinfeld modules defined over Tate algebras that we introduce (the coefficients can be chosen in a Tate algebra). This enables us to generalize Anderson's log-algebraicity Theorem and an analogue of Herbrand-Ribet Theorem recently obtained by Taelman.

show abstract

“…The formula. The next Theorem directly follows from Theorem 11.3, proved in the appendix by Florent Demeslay, by means of Proposition 5.9 and the isomorphism (16).…”

Section: 3mentioning

confidence: 84%

Arithmetic of positive characteristic -series values in Tate algebras

Pellarin²,

et al. 2015

View full text Add to dashboard Cite

show abstract

“…More recently, Perkins [14] investigated the properties of certain special polynomials associated to variants of the functions L(χ β t , α) with α ≤ 0 which turn out to be polynomial. He notably studied the growth of their degrees.…”

Section: Introduction Resultsmentioning

confidence: 99%

Functional identities for L-series values in positive characteristic

Anglès

Pellarin²

2014

Journal of Number Theory

View full text Add to dashboard Cite

show abstract

“…Multivariate Special Polynomials. The results of this note expand upon the author's work in [11] and have been ported over from the author's dissertation [13]. We study the multivariate special polynomials, defined for non-negative integers β 1 , .…”

Section: 2mentioning

confidence: 65%

An exact degree for multivariate special polynomials

Perkins¹

2014

Journal of Number Theory

Self Cite

View full text Add to dashboard Cite

We introduce certain special polynomials in an arbitrary number of indeterminates over a finite field. These polynomials generalize the special polynomials associated to the Goss zeta function and Goss-Dirichlet $L$-functions over the ring of polynomials in one indeterminate over a finite field and also capture the special values at non-positive integers of $L$-series associated to Drinfeld modules over Tate algebras defined over the same ring. We compute the exact degree in $t_0$ of these special polynomials and show that this degree is an invariant for a natural action of Goss' group of digit permutations. Finally, we characterize the vanishing of these multivariate special polynomials at $t_0=1$. This gives rise to a notion of trivial zeros for our polynomials generalizing that of the Goss zeta function mentioned above.Comment: 8 page

show abstract

On Pellarin’s $L$-series

Cited by 14 publications

References 13 publications

Arithmetic of positive characteristic -series values in Tate algebras

Arithmetic of positive characteristic -series values in Tate algebras

Functional identities for L-series values in positive characteristic

An exact degree for multivariate special polynomials

Contact Info

Product

Resources

About