We obtain a formula for the p-adic valuation of weighted moments of central L-values of holomorphic cusp forms twisted by Dirichlet characters of order p. In some cases we give an arithmetic interpretation of the constants in the formula. The result is obtained via the study of the digit map, turning a horizontal p-adic measure into a vertical one, applied to the horizontal p-adic L-functions as defined by Kriz and Nordentoft (Horizontal p-adic L-functions, 2023).
p-adic moments of L-functions / D.J. Kriz, A. Christian Nordentoft. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - 75:(2026 Mar 09), pp. 75.1-75.21. [10.1007/s12215-025-01365-8]
p-adic moments of L-functions
D.J. Kriz
Primo
;
2026
Abstract
We obtain a formula for the p-adic valuation of weighted moments of central L-values of holomorphic cusp forms twisted by Dirichlet characters of order p. In some cases we give an arithmetic interpretation of the constants in the formula. The result is obtained via the study of the digit map, turning a horizontal p-adic measure into a vertical one, applied to the horizontal p-adic L-functions as defined by Kriz and Nordentoft (Horizontal p-adic L-functions, 2023).
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