2024/12/01 by Thu Ha Trieu, Trieu, Thu Ha
Engineering · Mathematics · Computer Science · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Digital Image Processing Techniques
paper · pdf · doi:10.48550/arxiv.2412.00893
We express the Mahler measure of an exact polynomial in arbitrarily many variables in terms of Deligne-Beilinson cohomology. We then focus on the relationship between the Mahler measure of four-variable exact polynomials and the special value of the L-function of K3 surfaces at s = 4. This result extends the three-variable case studied in \citeTri23. Finally, we prove, under Beilinson's conjecture, that the Mahler measure of the polynomial (x+1)(y+1)(z+1) + t is expressed in terms of the Riemann zeta function and the L-function of the modular form of weight 3 and level 7.