Exotic approximate identities and Maass forms

Chamizo, Fernando; Raboso, Dulcinea; Ruiz-Cabello, Serafín

doi:10.4064/aa159-1-2

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Proof Of the Main Results1

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Cited by 2 publications

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“…The key argument is a simple one and it is summarized in the following result. We merely sketch the details of the proof because it is essentially contained in that of [, Lemma 2.3] (see also [, § 5] and [, Lemma 2.2]). Lemma For

0 < v < V

consider the function

F : {double-struckH}^{2} \to R

given by

F false(z, w false) = \frac{1}{4 π v} \int_{double-struckH} χ_{V} (u false(z, ζ false)) χ_{v} (u false(ζ, w false)) d μ false(ζ false) .

Then there exists

f : [0, \infty) \to R

such that

F (z, w) = f (u (z, w))

and

χ_{V^{-}} ⩽ f ⩽ χ_{V^{+}} where V^{\pm} = {(() \sqrt{V (1 + v)} \pm \sqrt{v (1 + V)})}^{2} .

Moreover, the S‐HC transform of

f

h_{V} h_{v}

.…”

Section: Proof Of the Main Resultsmentioning

confidence: 99%

Sums of squares in real quadratic fields and Hilbert modular groups

Chamizo

Miatello

2020

Bull. London Math. Soc.

Self Cite

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0 < v < V

consider the function

F : {double-struckH}^{2} \to R

given by

F false(z, w false) = \frac{1}{4 π v} \int_{double-struckH} χ_{V} (u false(z, ζ false)) χ_{v} (u false(ζ, w false)) d μ false(ζ false) .

Then there exists

f : [0, \infty) \to R

such that

F (z, w) = f (u (z, w))

and

χ_{V^{-}} ⩽ f ⩽ χ_{V^{+}} where V^{\pm} = {(() \sqrt{V (1 + v)} \pm \sqrt{v (1 + V)})}^{2} .

Moreover, the S‐HC transform of

f

h_{V} h_{v}

.…”

Section: Proof Of the Main Resultsmentioning

confidence: 99%

Sums of squares in real quadratic fields and Hilbert modular groups

Chamizo

Miatello

2020

Bull. London Math. Soc.

Self Cite

View full text Add to dashboard Cite

show abstract

On the Kuznetsov formula

Chamizo

Raboso

2015

Journal of Functional Analysis

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Exotic approximate identities and Maass forms

Cited by 2 publications

References 6 publications

Sums of squares in real quadratic fields and Hilbert modular groups

Sums of squares in real quadratic fields and Hilbert modular groups

On the Kuznetsov formula

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