Eisenstein series, p-adic modular functions, and overconvergence

Institut for Matematiske Fag

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

I: Research in Number Theory, Bind 7, Nr. 4, 65, 2021.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Kiming, I & Rustom, N 2021, 'Eisenstein series, p-adic modular functions, and overconvergence', Research in Number Theory, bind 7, nr. 4, 65. https://doi.org/10.1007/s40993-021-00292-8

APA

Kiming, I., & Rustom, N. (2021). Eisenstein series, p-adic modular functions, and overconvergence. Research in Number Theory, 7(4), [65]. https://doi.org/10.1007/s40993-021-00292-8

Vancouver

Kiming I, Rustom N. Eisenstein series, p-adic modular functions, and overconvergence. Research in Number Theory. 2021;7(4). 65. https://doi.org/10.1007/s40993-021-00292-8

Author

Kiming, Ian ; Rustom, Nadim. / Eisenstein series, p-adic modular functions, and overconvergence. I: Research in Number Theory. 2021 ; Bind 7, Nr. 4.

Bibtex

@article{2170bf2abd5f4fffb2d5bf3df510dc43,

title = "Eisenstein series, p-adic modular functions, and overconvergence",

abstract = "Let p be a prime ≥ 5. We establish explicit rates of overconvergence for some members of the “Eisenstein family”, notably for the p-adic modular function V(E(1,0)∗)/E(1,0)∗ (V the p-adic Frobenius operator) that plays a pivotal role in Coleman{\textquoteright}s theory of p-adic families of modular forms. The proof goes via an in-depth analysis of rates of overconvergence of p-adic modular functions of form V(Ek) / Ek where Ek is the classical Eisenstein series of level 1 and weight k divisible by p- 1. Under certain conditions, we extend the latter result to a vast generalization of a theorem of Coleman–Wan regarding the rate of overconvergence of V(Ep-1) / Ep-1. We also comment on previous results in the literature. These include applications of our results for the primes 5 and 7.",

keywords = "Colman-Mazur eigencurve, Eisenstein series, Overconvergent modular forms",

author = "Ian Kiming and Nadim Rustom",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/s40993-021-00292-8",

language = "English",

volume = "7",

journal = "Research in Number Theory",

issn = "2363-9555",

publisher = "Springer",

number = "4",

}

RIS

TY - JOUR

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

AU - Kiming, Ian

AU - Rustom, Nadim

PY - 2021

Y1 - 2021

N2 - Let p be a prime ≥ 5. We establish explicit rates of overconvergence for some members of the “Eisenstein family”, notably for the p-adic modular function V(E(1,0)∗)/E(1,0)∗ (V the p-adic Frobenius operator) that plays a pivotal role in Coleman’s theory of p-adic families of modular forms. The proof goes via an in-depth analysis of rates of overconvergence of p-adic modular functions of form V(Ek) / Ek where Ek is the classical Eisenstein series of level 1 and weight k divisible by p- 1. Under certain conditions, we extend the latter result to a vast generalization of a theorem of Coleman–Wan regarding the rate of overconvergence of V(Ep-1) / Ep-1. We also comment on previous results in the literature. These include applications of our results for the primes 5 and 7.

AB - Let p be a prime ≥ 5. We establish explicit rates of overconvergence for some members of the “Eisenstein family”, notably for the p-adic modular function V(E(1,0)∗)/E(1,0)∗ (V the p-adic Frobenius operator) that plays a pivotal role in Coleman’s theory of p-adic families of modular forms. The proof goes via an in-depth analysis of rates of overconvergence of p-adic modular functions of form V(Ek) / Ek where Ek is the classical Eisenstein series of level 1 and weight k divisible by p- 1. Under certain conditions, we extend the latter result to a vast generalization of a theorem of Coleman–Wan regarding the rate of overconvergence of V(Ep-1) / Ep-1. We also comment on previous results in the literature. These include applications of our results for the primes 5 and 7.

KW - Colman-Mazur eigencurve

KW - Eisenstein series

KW - Overconvergent modular forms

U2 - 10.1007/s40993-021-00292-8

DO - 10.1007/s40993-021-00292-8

M3 - Journal article

AN - SCOPUS:85116403242

VL - 7

JO - Research in Number Theory

JF - Research in Number Theory

SN - 2363-9555

IS - 4

M1 - 65

ER -

ID: 284172945