Kronecker limit formulas for parabolic, hyperbolic and elliptic Eisenstein series via Borcherds products

Pippich, Anna-Maria von; Schwagenscheidt, Markus; Völz, Fabian

doi:10.1016/j.jnt.2021.01.010

Cited by 5 publications

(1 citation statement)

References 23 publications

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“…We remark that in weight 0, the analytic continuation to s = 1 was established in all three cases, see [13,Theorem 4.2], [17,Section 4], [18,Theorem 1.2], [14,Appendix B]. Hence, it seems natural to ask wether similar results hold in weight 2 or higher, overleaping the "point of symmetry" k = 1.…”

Section: Introductionmentioning

confidence: 88%

Eisenstein series of even weight $k \geq 2$ and integral binary quadratic forms

Mono

2020

Preprint

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In a recent paper [14], Matsusaka investigated parabolic, elliptic, and hyperbolic Eisenstein series in weight 2. He provided the analytic continuation to s = 0 in the elliptic case, and conjectured an expression describing the same continuation in the hyperbolic case. We extend Matsusakas setting to general weight k ≥ 2, and embed his Eisenstein series into a framework based on discriminants of integral binary quadratic forms. Lastly, we compute the Fourier expansion of our Eisenstein series in the hyperbolic case by adapting Zagiers method [22, Section 2], and using results of Andersen and Duke [2].

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Section: Introductionmentioning

confidence: 88%

Eisenstein series of even weight $k \geq 2$ and integral binary quadratic forms

Mono

2020

Preprint

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Weight $$\mathbf {1/2}$$ multiplier systems for the group $$\mathbf {\Gamma _0^+({\varvec{p}})}$$ and a geometric formulation

Mertens,

Norfleet

2024

Arch. Math.

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We construct a weight 1/2 multiplier system for the group $$\Gamma _0^+(p)$$ Γ 0 + ( p ) , the normalizer of the congruence subgroup $$\Gamma _0(p)$$ Γ 0 ( p ) where p is an odd prime, and we define an analogue of the eta function and Rademacher symbol and relate it to the geometry of edge paths in a triangulation of the upper half-plane.

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Locally harmonic Maass forms of positive even weight

Mono

2023

Isr. J. Math.

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We twist Zagier’s function fk,D by a sign function and a genus character. Assuming weight 0 < k ≡ 2 (mod 4), and letting D be a positive non-square discriminant, we prove that the obstruction to modularity caused by the sign function can be corrected obtaining a locally harmonic Maaß form or a local cusp form of the same weight. In addition, we provide an alternative representation of our new function in terms of a twisted trace of modular cycle integrals of a Poincaré series due to Petersson.

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Kronecker limit formulas for parabolic, hyperbolic and elliptic Eisenstein series via Borcherds products

Cited by 5 publications

References 23 publications

Eisenstein series of even weight $k \geq 2$ and integral binary quadratic forms

Eisenstein series of even weight $k \geq 2$ and integral binary quadratic forms

Weight $$\mathbf {1/2}$$ multiplier systems for the group $$\mathbf {\Gamma _0^+({\varvec{p}})}$$ and a geometric formulation

Locally harmonic Maass forms of positive even weight

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