Taylor coefficients of the Jacobi θ3(q) function

Wakhare, Tanay; Vignat, Christophe

doi:10.1016/j.jnt.2020.03.002

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2024

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Cited by 3 publications

(2 citation statements)

References 15 publications

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“…around τ 0 = i (we refer to [2,8,10,15,16]). Romik defined (d(n)) ∞ n=0 to be the sequence such that…”

Section: Introduction and Resultsmentioning

confidence: 99%

$p$-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on $\Gamma_1(4)$

Kim

Lee

2023

Taiwanese J. Math.

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For a prime p ≡ 3 (mod 4) and m ≥ 2, Romik raised a question about whether the Taylor coefficients around √ −1 of the classical Jacobi theta function θ 3 eventually vanish modulo p m . This question can be extended to a class of modular forms of half-integral weight on Γ 1 (4) and CM points; in this paper, we prove an affirmative answer to it for primes p ≥ 5. Our result is also a generalization of the results of Larson and Smith for modular forms of integral weight on SL 2 (Z).

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“…around τ 0 = i (we refer to [2,8,10,15,16]). Romik defined (d(n)) ∞ n=0 to be the sequence such that…”

Section: Introduction and Resultsmentioning

confidence: 99%

$p$-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on $\Gamma_1(4)$

Kim

Lee

2023

Taiwanese J. Math.

View full text Add to dashboard Cite

show abstract

“…around τ 0 = i (we refer to [8], [10], [2], [15], and [16]). Romik defined (d(n)) ∞ n=0 to be the sequence such that…”

mentioning

confidence: 99%

$p$-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on $Γ_1(4)$

Kim¹,

Lee²

2021

Preprint

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For a prime p ≡ 3 (mod 4) and m ≥ 2, Romik raised a question about whether the Taylor coefficients around √ −1 of the classical Jacobi theta function θ 3 eventually vanish modulo p m . This question can be extended to a class of modular forms of half-integral weight on Γ 1 (4) and CM points; in this paper, we prove an affirmative answer to it for primes p ≥ 5.Our result is also a generalization of the results of Larson and Smith for modular forms of integral weight on SL 2 (Z).

show abstract

Dubious Identities: A Visit to the Borwein Zoo

Bradshaw,

Vignat

2024

The American Mathematical Monthly

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Taylor coefficients of the Jacobi θ3(q) function

Cited by 3 publications

References 15 publications

$p$-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on $\Gamma_1(4)$

$p$-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on $\Gamma_1(4)$

$p$-adic Properties for Taylor Coefficients of Half-integral Weight Modular Forms on $Γ_1(4)$

Dubious Identities: A Visit to the Borwein Zoo

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