On the Gross-Stark Conjecture
| Autor: | Mahesh Kakde, Kevin Ventullo, Samit Dasgupta |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Conjecture
Mathematics - Number Theory Mathematics::Number Theory 010102 general mathematics Abelian extension Term (logic) 01 natural sciences Combinatorics math.NT Mathematics (miscellaneous) Character (mathematics) 0103 physical sciences FOS: Mathematics Number Theory (math.NT) 010307 mathematical physics 0101 mathematics Statistics Probability and Uncertainty Scaling Mathematics Real field |
| Zdroj: | Dasgupta, S, Kakde, M & Ventullo, K 2018, ' On the Gross-Stark Conjecture ', ANNALS OF MATHEMATICS, vol. 188, no. 3, pp. 833-870 . https://doi.org/10.4007/annals.2018.188.3.3 |
| Popis: | In 1980, Gross conjectured a formula for the expected leading term at $s=0$ of the Deligne--Ribet $p$-adic $L$-function associated to a totally even character $\psi$ of a totally real field $F$. The conjecture states that after scaling by $L(\psi \omega^{-1}, 0)$, this value is equal to a $p$-adic regulator of units in the abelian extension of $F$ cut out by $\psi \omega^{-1}$. In this paper, we prove Gross's conjecture. Comment: 38 pages |
| Databáze: | OpenAIRE |
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