# Enumerating graded ideals in graded rings associated to free nilpotent Lie rings

Enumerating graded ideals in graded rings associated to free nilpotent Lie rings We compute the zeta functions enumerating graded ideals in the graded Lie rings associated with the free d-generator Lie rings $$\mathfrak {f}_{c,d}$$ f c , d of nilpotency class c for all $$c\leqslant 2$$ c ⩽ 2 and for $$(c,d)\in \{(3,3),(3,2),(4,2)\}$$ ( c , d ) ∈ { ( 3 , 3 ) , ( 3 , 2 ) , ( 4 , 2 ) } . We apply our computations to obtain information about $$\mathfrak {p}$$ p -adic, reduced, and topological zeta functions, in particular pertaining to their degrees and some special values. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

# Enumerating graded ideals in graded rings associated to free nilpotent Lie rings

, Volume 290 (4) – May 30, 2018
28 pages

Publisher
Springer Journals
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
D.O.I.
10.1007/s00209-018-2062-9
Publisher site
See Article on Publisher Site

### Abstract

We compute the zeta functions enumerating graded ideals in the graded Lie rings associated with the free d-generator Lie rings $$\mathfrak {f}_{c,d}$$ f c , d of nilpotency class c for all $$c\leqslant 2$$ c ⩽ 2 and for $$(c,d)\in \{(3,3),(3,2),(4,2)\}$$ ( c , d ) ∈ { ( 3 , 3 ) , ( 3 , 2 ) , ( 4 , 2 ) } . We apply our computations to obtain information about $$\mathfrak {p}$$ p -adic, reduced, and topological zeta functions, in particular pertaining to their degrees and some special values.

### Journal

Mathematische ZeitschriftSpringer Journals

Published: May 30, 2018

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