Eisenstein series, p-adic modular functions, and overconvergence, II

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Eisenstein series, p-adic modular functions, and overconvergence, II. / Kiming, Ian; Rustom, Nadim.

In: Research in Number Theory, Vol. 10, No. 1, 4, 2024, p. 1-14.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Kiming, I & Rustom, N 2024, 'Eisenstein series, p-adic modular functions, and overconvergence, II', Research in Number Theory, vol. 10, no. 1, 4, pp. 1-14. https://doi.org/10.1007/s40993-023-00491-5

APA

Kiming, I., & Rustom, N. (2024). Eisenstein series, p-adic modular functions, and overconvergence, II. Research in Number Theory, 10(1), 1-14. [4]. https://doi.org/10.1007/s40993-023-00491-5

Vancouver

Kiming I, Rustom N. Eisenstein series, p-adic modular functions, and overconvergence, II. Research in Number Theory. 2024;10(1):1-14. 4. https://doi.org/10.1007/s40993-023-00491-5

Author

Kiming, Ian ; Rustom, Nadim. / Eisenstein series, p-adic modular functions, and overconvergence, II. In: Research in Number Theory. 2024 ; Vol. 10, No. 1. pp. 1-14.

Bibtex

@article{39e35ec40c184898878b56825006bc8a,
title = "Eisenstein series, p-adic modular functions, and overconvergence, II",
abstract = "Let p be a prime number. Continuing and extending our previous paper with the same title, we prove explicit rates of overconvergence for modular functions of the form where is a classical, normalized Eisenstein series on and V the p-adic Frobenius operator. In particular, we extend our previous paper to the primes 2 and 3. For these primes our main theorem improves somewhat upon earlier results by Emerton, Buzzard and Kilford, and Roe. We include a detailed discussion of those earlier results as seen from our perspective. We also give some improvements to our earlier paper for primes . Apart from establishing these improvements, our main purpose here is also to show that all of these results can be obtained by a uniform method, i.e., a method where the main points in the argumentation is the same for all primes. We illustrate the results by some numerical examples.",
author = "Ian Kiming and Nadim Rustom",
year = "2024",
doi = "10.1007/s40993-023-00491-5",
language = "English",
volume = "10",
pages = "1--14",
journal = "Research in Number Theory",
issn = "2363-9555",
publisher = "Springer",
number = "1",

}

RIS

TY - JOUR

T1 - Eisenstein series, p-adic modular functions, and overconvergence, II

AU - Kiming, Ian

AU - Rustom, Nadim

PY - 2024

Y1 - 2024

N2 - Let p be a prime number. Continuing and extending our previous paper with the same title, we prove explicit rates of overconvergence for modular functions of the form where is a classical, normalized Eisenstein series on and V the p-adic Frobenius operator. In particular, we extend our previous paper to the primes 2 and 3. For these primes our main theorem improves somewhat upon earlier results by Emerton, Buzzard and Kilford, and Roe. We include a detailed discussion of those earlier results as seen from our perspective. We also give some improvements to our earlier paper for primes . Apart from establishing these improvements, our main purpose here is also to show that all of these results can be obtained by a uniform method, i.e., a method where the main points in the argumentation is the same for all primes. We illustrate the results by some numerical examples.

AB - Let p be a prime number. Continuing and extending our previous paper with the same title, we prove explicit rates of overconvergence for modular functions of the form where is a classical, normalized Eisenstein series on and V the p-adic Frobenius operator. In particular, we extend our previous paper to the primes 2 and 3. For these primes our main theorem improves somewhat upon earlier results by Emerton, Buzzard and Kilford, and Roe. We include a detailed discussion of those earlier results as seen from our perspective. We also give some improvements to our earlier paper for primes . Apart from establishing these improvements, our main purpose here is also to show that all of these results can be obtained by a uniform method, i.e., a method where the main points in the argumentation is the same for all primes. We illustrate the results by some numerical examples.

U2 - 10.1007/s40993-023-00491-5

DO - 10.1007/s40993-023-00491-5

M3 - Journal article

VL - 10

SP - 1

EP - 14

JO - Research in Number Theory

JF - Research in Number Theory

SN - 2363-9555

IS - 1

M1 - 4

ER -

ID: 375965647