Mahler measures and $L$-functions of $K3$ surfaces
| Autor: | Trieu, Thu Ha |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We relate the Mahler measure of exact polynomials in arbitrary variables to the Deligne cohomology of the Maillot variety using the Goncharov polylogarithmic complexes. In the four-variable case, we further study the relationship between the Mahler measure and special values of $L$-functions of $K3$ surfaces. The method involves a construction of an element in the motivic cohomology of $K3$ surfaces. We apply our method to the exact polynomial $(x+1)(y+1)(z+1) + t$. Comment: 32 pages. Comments are welcome! |
| Databáze: | arXiv |
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