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Newform Eisenstein congruences of local origin

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Newform Eisenstein congruences of local origin. / Fretwell, Dan; Roberts, Jenny.
In: The Ramanujan Journal, Vol. 64, No. 2, 01.06.2024, p. 505-527.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Fretwell, D & Roberts, J 2024, 'Newform Eisenstein congruences of local origin', The Ramanujan Journal, vol. 64, no. 2, pp. 505-527. https://doi.org/10.1007/s11139-024-00838-1

APA

Fretwell, D., & Roberts, J. (2024). Newform Eisenstein congruences of local origin. The Ramanujan Journal, 64(2), 505-527. https://doi.org/10.1007/s11139-024-00838-1

Vancouver

Fretwell D, Roberts J. Newform Eisenstein congruences of local origin. The Ramanujan Journal. 2024 Jun 1;64(2):505-527. Epub 2024 Mar 23. doi: 10.1007/s11139-024-00838-1

Author

Fretwell, Dan ; Roberts, Jenny. / Newform Eisenstein congruences of local origin. In: The Ramanujan Journal. 2024 ; Vol. 64, No. 2. pp. 505-527.

Bibtex

@article{44dfd515fb814e5f9283a1205afe6efa,
title = "Newform Eisenstein congruences of local origin",
abstract = "We give a general conjecture concerning the existence of Eisenstein congruences between weight k≥3 newforms of square-free level NM and weight k new Eisenstein series of square-free level N. Our conjecture allows the forms to have arbitrary character χ of conductor N. The special cases M=1 and M=p prime are fully proved, with partial results given in general. We also consider the relation with the Bloch–Kato conjecture, and finish with computational examples demonstrating cases of our conjecture that have resisted proof.",
keywords = "11F30, 11F33, 11F80, 11R34, Congruences, Eisenstein series, Galois representations, Modular forms, Primary 11F11, Secondary 11F67",
author = "Dan Fretwell and Jenny Roberts",
year = "2024",
month = jun,
day = "1",
doi = "10.1007/s11139-024-00838-1",
language = "English",
volume = "64",
pages = "505--527",
journal = "The Ramanujan Journal",
number = "2",

}

RIS

TY - JOUR

T1 - Newform Eisenstein congruences of local origin

AU - Fretwell, Dan

AU - Roberts, Jenny

PY - 2024/6/1

Y1 - 2024/6/1

N2 - We give a general conjecture concerning the existence of Eisenstein congruences between weight k≥3 newforms of square-free level NM and weight k new Eisenstein series of square-free level N. Our conjecture allows the forms to have arbitrary character χ of conductor N. The special cases M=1 and M=p prime are fully proved, with partial results given in general. We also consider the relation with the Bloch–Kato conjecture, and finish with computational examples demonstrating cases of our conjecture that have resisted proof.

AB - We give a general conjecture concerning the existence of Eisenstein congruences between weight k≥3 newforms of square-free level NM and weight k new Eisenstein series of square-free level N. Our conjecture allows the forms to have arbitrary character χ of conductor N. The special cases M=1 and M=p prime are fully proved, with partial results given in general. We also consider the relation with the Bloch–Kato conjecture, and finish with computational examples demonstrating cases of our conjecture that have resisted proof.

KW - 11F30

KW - 11F33

KW - 11F80

KW - 11R34

KW - Congruences

KW - Eisenstein series

KW - Galois representations

KW - Modular forms

KW - Primary 11F11

KW - Secondary 11F67

U2 - 10.1007/s11139-024-00838-1

DO - 10.1007/s11139-024-00838-1

M3 - Journal article

VL - 64

SP - 505

EP - 527

JO - The Ramanujan Journal

JF - The Ramanujan Journal

IS - 2

ER -