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
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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