Journal: Acta Arithmetica

Abbreviation

Acta Arith.

Publisher

Instytut Matematyczny

Journal Volumes

ISSN

0065-1036
1730-6264

Description

Filters

2020 - 20233
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Publications 1 - 3 of 3
  • Cycle integrals of the Parson Poincaré series and intersection angles of geodesics on modular curves
    Item type: Journal Article
    Lägeler, Alessandro; Schwagenscheidt, Markus (2022)
    Acta Arithmetica
    We prove a geometric formula for the cycle integrals of Parson’s weight 2k modular integrals in terms of the intersection angles of geodesics on modular curves. Our result is an analog for modular integrals of a classical formula for the cycle integrals of certain hyperbolic Poincaré series, due to Katok. On the other hand, it extends a recent geometric formula of Matsusaka and of Duke, Imamoḡlu, and Tóth for the cycle integrals of weight 2 modular integrals.
  • Ultra-short sums of trace functions
    Item type: Journal Article
    Kowalski, Emmanuel; Untrau, Théo (2023)
    Acta Arithmetica
    We generalize results of Duke, Garcia, Hyde, Lutz and others on the distribution of sums of roots of unity related to Gaussian periods to obtain equidistribution of similar sums over zeros of arbitrary integral polynomials. We also interpret these results in terms of trace functions, and generalize them to higher rank trace functions.
  • Transformation laws for modular Dedekind symbols
    Item type: Journal Article
    Burrin, Claire; Jorgenson, Jay; O'Sullivan, Cormac; et al. (2020)
    Acta Arithmetica
    We establish transformation laws for generalized Dedekind sums associated to the Kronecker limit function of non-holomorphic Eisenstein series and their higher-order variants. These results apply to general Fuchsian groups of the first kind, and examples are provided in the cases of the Hecke triangle groups, the Hecke congruence groups Γ0(N), and the non-congruence arithmetic groups Γ0(N)+.
Publications 1 - 3 of 3