Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation

Altan Erdoğan

doi:10.36753/mathenot.794789

Research Article

Year 2021, , 74 - 80, 01.06.2021

Altan Erdoğan

https://doi.org/10.36753/mathenot.794789

Abstract

References

[1] Kubota, T., Leopold H.W.; Eine p-adische Theorie der Zetawerte, I. Journ. Reine Angew. Math., 214/215, 328-339, (1964).
[2] Coleman, R.F.: Dilogarithms, Regulators and p-adic L-functions, Invent. Math.,69, 171-208, (1982).
[3] Washington, L.C.: Introduction to Cyclotomic Fields, Springer-Verlag, New York, (1982).
[4] Diamond, J.: The p-adic Gamma Measures, Proc. Amer. Math. Soc., 75(2), 211-217, (1979).
[5] Diamond, J.: The p-adic Log Gamma Function and p-adic Euler Constants, Trans. Amer. Math. Soc., 233, 321-337, (1977).
[6] Lang, S.: Introduction to Modular Forms, Springer-Verlag, Berlin Heidelberg, (1976).
[7] Katz, N.: p-Adic Properties of Modular Schemes and Modular Forms, In: Kuijk W., Serre JP. (eds) Modular Functions of One Variable III, Lecture Notes in Mathematics, vol 350. Springer, Berlin, Heidelberg, (1973).
[8] Katz, N.: p-adic L-functions via Moduli of Elliptic Curves, Proc. 1974 AMS Arcata Summer Institute in Algebraic Geometry, PSPM 29, AMS, Providence (1975).
[9] Koblitz, N.: p-adic Numbers, p-adic Analysis and Zeta-Functions, Springer-Verlag, New York, (1984).
[10] Koblitz, N.: p-adic Analysis: a Short Course on RecentWork, London Mathematical Society Lecture Note 46, Cambridge University Press, Cambridge, New York, (1980).

Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation

Year 2021, , 74 - 80, 01.06.2021

Altan Erdoğan

https://doi.org/10.36753/mathenot.794789

Abstract

The $p$-adic distributions attached to ordinary functions defined on $p$-adic fields with moderate variation are studied. We first give a sufficient growth condition on ordinary functions to construct $p$-adic distributions. Then a moderate variation condition on functions for regularization of these $p$-adic distributions is imposed which provides a general method to construct $p$-adic measures. The $p$-adic integrals against these measures are also explicitly transformed to integrals against Bernoulli measures.

Keywords

p-adic analysis, p-adic integration, Bernoulli measures, p-adic Gamma measures

References

[1] Kubota, T., Leopold H.W.; Eine p-adische Theorie der Zetawerte, I. Journ. Reine Angew. Math., 214/215, 328-339, (1964).
[2] Coleman, R.F.: Dilogarithms, Regulators and p-adic L-functions, Invent. Math.,69, 171-208, (1982).
[3] Washington, L.C.: Introduction to Cyclotomic Fields, Springer-Verlag, New York, (1982).
[4] Diamond, J.: The p-adic Gamma Measures, Proc. Amer. Math. Soc., 75(2), 211-217, (1979).
[5] Diamond, J.: The p-adic Log Gamma Function and p-adic Euler Constants, Trans. Amer. Math. Soc., 233, 321-337, (1977).
[6] Lang, S.: Introduction to Modular Forms, Springer-Verlag, Berlin Heidelberg, (1976).
[7] Katz, N.: p-Adic Properties of Modular Schemes and Modular Forms, In: Kuijk W., Serre JP. (eds) Modular Functions of One Variable III, Lecture Notes in Mathematics, vol 350. Springer, Berlin, Heidelberg, (1973).
[8] Katz, N.: p-adic L-functions via Moduli of Elliptic Curves, Proc. 1974 AMS Arcata Summer Institute in Algebraic Geometry, PSPM 29, AMS, Providence (1975).
[9] Koblitz, N.: p-adic Numbers, p-adic Analysis and Zeta-Functions, Springer-Verlag, New York, (1984).
[10] Koblitz, N.: p-adic Analysis: a Short Course on RecentWork, London Mathematical Society Lecture Note 46, Cambridge University Press, Cambridge, New York, (1980).

There are 10 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Articles
Authors	Altan Erdoğan 0000-0001-5113-1906
Publication Date	June 1, 2021
Submission Date	September 14, 2020
Acceptance Date	December 22, 2020
Published in Issue	Year 2021

Cite

APA	Erdoğan, A. (2021). Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation. Mathematical Sciences and Applications E-Notes, 9(2), 74-80. https://doi.org/10.36753/mathenot.794789
AMA	Erdoğan A. Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation. Math. Sci. Appl. E-Notes. June 2021;9(2):74-80. doi:10.36753/mathenot.794789
Chicago	Erdoğan, Altan. “Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation”. Mathematical Sciences and Applications E-Notes 9, no. 2 (June 2021): 74-80. https://doi.org/10.36753/mathenot.794789.
EndNote	Erdoğan A (June 1, 2021) Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation. Mathematical Sciences and Applications E-Notes 9 2 74–80.
IEEE	A. Erdoğan, “Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation”, Math. Sci. Appl. E-Notes, vol. 9, no. 2, pp. 74–80, 2021, doi: 10.36753/mathenot.794789.
ISNAD	Erdoğan, Altan. “Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation”. Mathematical Sciences and Applications E-Notes 9/2 (June 2021), 74-80. https://doi.org/10.36753/mathenot.794789.
JAMA	Erdoğan A. Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation. Math. Sci. Appl. E-Notes. 2021;9:74–80.
MLA	Erdoğan, Altan. “Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation”. Mathematical Sciences and Applications E-Notes, vol. 9, no. 2, 2021, pp. 74-80, doi:10.36753/mathenot.794789.
Vancouver	Erdoğan A. Regularization of $p$-Adic Distributions Associated to Functions on $p$-Adic Fields With Moderate Variation. Math. Sci. Appl. E-Notes. 2021;9(2):74-80.