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Strong Subconvexity for Self-Dual GL(3) L-Functions

Yongxiao Lin, Ramon Moreira Nunes

In this paper, we prove strong subconvexity bounds for self-dual GL(3) L-functions in the t-aspect and for GL(3) x GL(2) L-functions in the GL(2)-spectral aspect. The bounds are strong in the sense that they are the natural limit of the moment method pioneered by Xiaoqing Li, modulo current knowledge on estimate for the second moment of GL(3) L-functions on the critical line.

OXFORD UNIV PRESS2022

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Let u(q)(g) be the small quantum group associated with a complex semisimple Lie algebra g and a primitive root of unity q, satisfying certain restrictions. We establish the equivalence between three different actions of g on the center of u(q)(g) and on the higher derived center of u(q)(g). Based on the triviality of this action for g = sl(2), sl(3), sl(4), we conjecture that, in finite type A, central elements of the small quantum group u(q)(Sl(n)) arise as the restriction of central elements in the big quantum group u(q)(sl(n)). We also study the role of an ideal z(Hig) known as the Higman ideal in the center of u(q)(g). We show that it coincides with the intersection of the Harish-Chandra center and its Fourier transform, and compute the dimension of z(Hig) in type A. As an illustration we provide a detailed explicit description of the derived center of u(q)(sl(2)) and its various symmetries.

SPRINGER INTERNATIONAL PUBLISHING AG2021

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CHIMERA: Combining Ring-LWE-based Fully Homomorphic Encryption Schemes

Dimitar Petkov Jetchev

This paper proposes a practical hybrid solution for combining and switching between three popular Ring-LWE-based FHE schemes: TFHE, B/FV and HEAAN. This is achieved by first mapping the different plaintext spaces to a common algebraic structure and then by applying efficient switching algorithms. This approach has many practical applications. First and foremost, it becomes an integral tool for the recent standardization initiatives of homomorphic schemes and common APIs. Then, it can be used in many real-life scenarios where operations of different nature and not achievable within a single FHE scheme have to be performed and where it is important to efficiently switch from one scheme to another. Finally, as a byproduct of our analysis we introduce the notion of a FHE module structure, that generalizes the notion of the external product, but can certainly be of independent interest in future research in FHE.

WALTER DE GRUYTER GMBH2020

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