Infinite product exponents for modular forms

Ali, Asra; Mani, Nitya

doi:10.1007/s40993-016-0050-x

Cited by 4 publications

(4 citation statements)

References 9 publications

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“…Existing results in the literature (e.g. [1]) do not seem sufficient to show that all elements of B 0 satisfy the restriction in Proposition 3.2. By Borcherds's isomorphism Theorem 3.1, showing all such functions do meet this restriction would be equivalent to proving a result on the non-vanishing of Fourier coefficients for some weight 1/2 weakly holomorphic modular forms on Γ 0 (4).…”

Section: A Proof Of Theorem 12 Via the Product Formulamentioning

confidence: 94%

Multiplicative independence of modular functions

Fowler

2020

Preprint

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We provide two new proofs of the multiplicative independence of pairwise distinct GL + 2 (Q)-translates of the modular j-function, a result due originally to Pila and Tsimerman. We are thereby able to extend their result to a wider class of modular functions. For modular functions f ∈ Q(j) belonging to this class, we deduce, for each n ≥ 1, the finiteness of n-tuples of f -special points that are multiplicatively dependent and minimal for this property. This generalises a theorem of Pila and Tsimerman on singular moduli. We then show how these results relate to the Zilber-Pink conjecture for subvarieties of the mixed Shimura variety Y (1) n × G n m and prove some special cases of this conjecture.

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Section: A Proof Of Theorem 12 Via the Product Formulamentioning

confidence: 94%

Multiplicative independence of modular functions

Fowler

2020

Preprint

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“…The present text was written in 2016 and it was distributed among few experts in the area. Since then there have been some developments and we knew of some other related works, see [1]. However, its main conjecture is still open, and so we decided to publish it as it is.…”

Section: Introductionmentioning

confidence: 99%

Product formulas for weight two newforms

Nikdelan

Movasati

2020

CadMAT

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“…Recently, Ali and Mani [3] proved an upper bound for exponents c(m) in the product expansion of f . The sum d|m dc(d) looks like a kind of convolution of σ 1 (m) (a sum of divisors) and σ f (m) (a sum of exponents of f ).…”

Section: Introductionmentioning

confidence: 99%

Values of harmonic weak Maass forms on Hecke orbits

Choi

Lee

Lim

2019

Journal of Mathematical Analysis and Applications

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Let q := e 2πiz , where z ∈ H. For an even integer k, let f (z) := q h ∞ m=1 (1 − q m ) c(m) be a meromorphic modular form of weight k on Γ 0 (N ). For a positive integer m, let T m be the mth Hecke operator and D be a divisor of a modular curve with level N . Both subjects, the exponents c(m) of a modular form and the distribution of the points in the support of T m .D, have been widely investigated.When the level N is one, Bruinier, Kohnen, and Ono obtained, in terms of the values of jinvariant function, identities between the exponents c(m) of a modular form and the points in the support of T m .D. In this paper, we extend this result to general Γ 0 (N ) in terms of values of harmonic weak Maass forms of weight 0. By the distribution of Hecke points, this applies to obtain an asymptotic behaviour of convolutions of sums of divisors of an integer and sums of exponents of a modular form.

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Infinite product exponents for modular forms

Cited by 4 publications

References 9 publications

Multiplicative independence of modular functions

Multiplicative independence of modular functions

Product formulas for weight two newforms

Values of harmonic weak Maass forms on Hecke orbits

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