New polynomials producing absolute pseudoprimes with any number of prime factors

Wolstenholme and Morley, Primes and Pseudoprimes

In this note, we prove $p^2$ is a Morley pseudoprime (of order 2) iff $p^2$ is a Wolstenholme pseudoprime (of order 2) iff $p$ is a Wolstenholme prime iff $p$ is a Morley prime. Concerning pseudoprimes of order 1 that are not powers of primes, only 3 are known of Wolstenholme's type and absolutely none have yet been identified of Morley's type.

枚举绝对 Lucas 伪素数

Tabulating Absolute Lucas Pseudoprimes

研究固定判别式下绝对 Lucas 伪素数的枚举问题，提出受 Carmichael 数启发的枚举算法及渐近分析，证明给定素因子集合下伪素数有限，并首次给出判别式 5 的枚举结果。

Producing Geometric Deformations of Orthogonal and Symplectic Galois Representations

For a representation of the absolute Galois group of the rationals over a finite field of characteristic $p$, we study the existence of a lift to characteristic zero that is geometric in the sense of the Fontaine-Mazur conjecture. For two-dimensional representations, Ramakrishna proved that under technical assumptions odd representations admit geometric lifts. We generalize this to higher dimensional orthogonal and symplectic representations. A key step is generalizing and studying a local deformation condition at $p$ arising from Fontaine-Laffaille theory.

Computable Absolutely Pisot Normal Numbers

We analyze the convergence order of an algorithm producing the digits of an absolutely normal number. Furthermore, we introduce a stronger concept of absolute normality by allowing Pisot numbers as bases, which leads to expansions with non-integer bases.