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Quaternionic families of Heegner points and $p$-adic $L$-functions
Matteo Longo, Paola Magrone, Eduardo Rocha Walchek
https://arxiv.org/abs/2510.04306 https://

Quaternionic families of Heegner points and $p$-adic $L$-functions
Following up a previous article of the authors which studies the interpolation of certain anticyclotomic $p$-adic $L$-functions associated to quaternionic modular forms in a Hida family, we extend the work of F. Castella on the interpolation and specialization of big Heegner points to the quaternionic setting. We prove an explicit reciprocity law relating the big $p$-adic $L$-function to the big Heegner points in this quaternionic setting.

Degenerate systems of three Brownian particles with asymmetric collisions: invariant measure of gaps
Thomas Dreyfus (UBE), Jules Flin (IP Paris, TSP, SOP - SAMOVAR), Sandro Franceschi (IP Paris, TSP, SOP - SAMOVAR)
https://arxiv.org/abs/2510.01807

Degenerate systems of three Brownian particles with asymmetric collisions: invariant measure of gaps
We consider a degenerate system of three Brownian particles undergoing asymmetric collisions. We study the gap process of this system and focus on its invariant measure. The gap process is described as an obliquely reflected degenerate Brownian motion in a quadrant. For all possible parameter cases, we compute the Laplace transform of the invariant measure, and fully characterize the conditions under which it belongs to the following classes: rational, algebraic, differentially finite, or diffe…