Geodesic
A twisted class number formula and Gross's special units over an imaginary quadratic field
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1333-1347 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $F/k$ be a finite abelian extension of number fields with $k$ imaginary quadratic. Let $O_F$ be the ring of integers of $F$ and $n\geq 2$ a rational integer. We construct a submodule in the higher odd-degree algebraic $K$-groups of $O_F$ using corresponding Gross's special elements. We show that this submodule is of finite index and prove that this index can be computed using the higher ``twisted'' class number of $F$, which is the cardinal of the finite algebraic $K$-group $K_{2n-2}(O_F)$.
Let $F/k$ be a finite abelian extension of number fields with $k$ imaginary quadratic. Let $O_F$ be the ring of integers of $F$ and $n\geq 2$ a rational integer. We construct a submodule in the higher odd-degree algebraic $K$-groups of $O_F$ using corresponding Gross's special elements. We show that this submodule is of finite index and prove that this index can be computed using the higher ``twisted'' class number of $F$, which is the cardinal of the finite algebraic $K$-group $K_{2n-2}(O_F)$.
DOI : 10.21136/CMJ.2023.0067-23
Classification : 11R70, 19F27
Keywords: algebraic $K$-theory; Dedekind zeta function; Artin $L$-function; Beilinson regulator; generalized index; Lichtenbaum conjecture 
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     author = {El Boukhari, Saad},
     title = {A twisted class number formula and {Gross's} special units over an imaginary quadratic field},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1333--1347},
     year = {2023},
     volume = {73},
     number = {4},
     doi = {10.21136/CMJ.2023.0067-23},
     zbl = {07790577},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2023.0067-23/}
}
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El Boukhari, Saad. A twisted class number formula and Gross's special units over an imaginary quadratic field. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1333-1347. doi: 10.21136/CMJ.2023.0067-23

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