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Aberg, Lucas; Samuels, Charles L.

The connections between consistent maps and measures. (English) Zbl 1533.11175

PUMP J. Undergrad. Res. 7, 60-78 (2024).

MSC:

11R04 Algebraic numbers; rings of algebraic integers
28A33 Spaces of measures, convergence of measures
11G50 Heights
46E10 Topological linear spaces of continuous, differentiable or analytic functions
46E15 Banach spaces of continuous, differentiable or analytic functions

Keywords:

consistent maps; measures; Weil height
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References:

[1] D. Allcock and J.D. Vaaler, A Banach space determined by the Weil height, Acta Arith., 136 (2009), 279-298, · Zbl 1228.11101
[2] A. Fröhlich, Local Fields. In Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Academic Press, 1967. · Zbl 1492.11160
[3] F.Q. Gouvêa, p-adic Numbers: An Introduction, Springer, 2020. · Zbl 1436.11001
[4] S. Kesavan, Measure and Integration, Hindustan Book Agency, 2019. · Zbl 1416.28001
[5] J. Neukirch, Algebraic Number Theory, Springer-Verlag, 1999. · Zbl 0956.11021
[6] A. Ostrowski, Über einige Lösungen der Funktionalgleichung ψ(x) • ψ(x) = ψ(xy), Acta Math., 41 (1916), 271-284. · JFM 46.0169.02
[7] W. Rudin, Real and Complex Analysis, McGraw-Hill Book Co., 1987. · Zbl 0925.00005
[8] C.L. Samuels. A classification of Q-valued linear functionals on Q × modulo units, Acta Arith., 205 (2022), 341-370. · Zbl 1529.11108
[9] C.L. Samuels, Consistent maps and their associated dual representation theorems, preprint available online at https://urldefense.com/v3/__https://drive.google. com/file/d/17ogsVpfzucjGcf307UDA8CAbMOcocodc/view?usp=drive_link__;!!P7nkOOY! vfuOZ5ewRY5k5yIfu6Dx8PXZ6FdZtZsuidRBIWOHSGKjN6Ijf8pE8l5EKeQzYAnuCUU1dH2C694E8TUbOAC_
[10] TIVgzUM\(. the pump journal of undergraduate research 7 (2023), 69-7\)
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