Genus and a riemann-roch theorem for non-commutative function fields in one variable

1981 ◽  
pp. 295-318 ◽  
Author(s):  
J. P. Van Deuren ◽  
J. Van Geel ◽  
F. Van Oystaeyen
Keyword(s):  
Function Fields ◽  
Roch Theorem

scholarly journals A NOTE ON THE GENUS OF GLOBAL FUNCTION FIELDS

2013 ◽  
Vol 55 (3) ◽  
pp. 559-565
Author(s):  
ZHENGJUN ZHAO ◽  
XIA WU
Keyword(s):  
Algebraic Geometry ◽  
Function Field ◽  
Elementary Proof ◽  
Function Fields ◽  
Drinfeld Module ◽  
Extension Field ◽  
Global Function ◽  
Global Function Fields ◽  
Roch Theorem ◽  
Stark Conjecture

AbstractTo give a relatively elementary proof of the Brumer–Stark conjecture in a function field context involving no algebraic geometry beyond the Riemann–Roch theorem for curves, Hayes Compos. Math., vol. 55, 1985, pp. 209–239) defined a normalizing field $H_\mathfrak{e}^*$ associated with a fixed sgn-normalized Drinfeld module and its extension field $K_\mathfrak{m}$, which is an analogue of cyclotomic function fields over a rational function field. We present explicitly in this note the formulae for the genus of the two fields and the maximal real subfield $H_\mathfrak{m}$ of $K_\mathfrak{m}$. In some sense, our results can be regarded as generalizations of formulae for the genus of classical cyclotomic function fields obtained by Hayes Trans. Amer. Math. Soc., vol. 189, 1974, pp. 77–91) and Kida and Murabayashi (Tokyo J. Math., vol. 14(1), 1991, pp. 45–56).

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.

On geometric Z p -extensions of function fields

1988 ◽  
Vol 62 (2) ◽  
pp. 145-161 ◽  
Author(s):  
R. Gold ◽  
H. Kisilevsky
Keyword(s):  
Function Fields

scholarly journals Correction to: Divisibility problems for function fields

2020 ◽  
Vol 160 (2) ◽  
pp. 519-521
Author(s):  
S. Baier ◽  
A. Bansal ◽  
R. K. Singh
Keyword(s):  
Function Fields
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