A rational reciprocity law over function fields

2016 ◽  
Vol 108 (3) ◽  
pp. 233-240
Author(s):  
Yoshinori Hamahata
Keyword(s):  
Function Fields ◽  
Reciprocity Law

Multiple Dedekind–Rademacher sums in function fields

2014 ◽  
Vol 10 (05) ◽  
pp. 1291-1307 ◽  
Author(s):  
Abdelmejid Bayad ◽  
Yoshinori Hamahata
Keyword(s):  
Function Fields ◽  
Dedekind Sums ◽  
Reciprocity Law ◽  
Higher Dimensional

In the previous paper, we introduced the higher-dimensional Dedekind sums in function fields, and established the reciprocity law. In this paper, we generalize our higher-dimensional Dedekind sums and establish the reciprocity law and the Petersson–Knopp identity.

THE RECIPROCITY LAW FOR THE TWISTED SECOND MOMENT OF DIRICHLET -FUNCTIONS OVER RATIONAL FUNCTION FIELDS

2018 ◽  
Vol 98 (3) ◽  
pp. 383-388 ◽  
Author(s):  
GORAN DJANKOVIĆ
Keyword(s):  
Rational Function ◽  
Function Fields ◽  
Mean Square ◽  
Irreducible Polynomials ◽  
Second Moment ◽  
Reciprocity Law ◽  
Second Moments ◽  
The Mean

We prove the reciprocity law for the twisted second moments of Dirichlet $L$-functions over rational function fields, corresponding to two irreducible polynomials. This formula is the analogue of the formulas for Dirichlet $L$-functions over $\mathbb{Q}$ obtained by Conrey [‘The mean-square of Dirichlet $L$-functions’, arXiv:0708.2699 [math.NT] (2007)] and Young [‘The reciprocity law for the twisted second moment of Dirichlet $L$-functions’, Forum Math. 23(6) (2011), 1323–1337].

Reciprocity Law for Compatible Systems of Abelian mod p Galois Representations

2005 ◽  
Vol 57 (6) ◽  
pp. 1215-1223 ◽  
Author(s):  
Chandrashekhar Khare
Keyword(s):  
Galois Representations ◽  
Function Fields ◽  
Arbitrary Dimension ◽  
Number Fields ◽  
Galois Groups ◽  
Reciprocity Law ◽  
Mod P

AbstractThe main result of the paper is a reciprocity law which proves that compatible systems of semisimple, abelianmod p representations (of arbitrary dimension) of absolute Galois groups of number fields, arise from Hecke characters. In the last section analogs for Galois groups of function fields of these results are explored, and a question is raised whose answer seems to require developments in transcendence theory in characteristic p.

scholarly journals ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS

2020 ◽  
pp. 1-10
Author(s):  
CLEMENS FUCHS ◽  
SEBASTIAN HEINTZE
Keyword(s):  
Number Field ◽  
Function Field ◽  
Function Fields ◽  
Linear Recurrence ◽  
Recurrence Sequence ◽  
Linear Recurrences ◽  
Field Case ◽  
Power Sum ◽  
Linear Recurrence Sequence

Abstract Let $ (G_n)_{n=0}^{\infty } $ be a nondegenerate linear recurrence sequence whose power sum representation is given by $ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $ . We prove a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions, $ |{G_n}| \geq ( \max _{j=1,\ldots ,t} |{\alpha _j}| )^{n(1-\varepsilon )} $ for $ n $ large enough.

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