280 citations · 1k across the 82 of their papers we have counts for
30 papers · 1 filter
Abelian varieties with isogenous reductions
Chandrashekhar B. Khare, Michael Larsen
If A and B are abelian varieties over a number field K such that there are non-trivial geometric homomorphisms of abelian varieties between reductions of A and B at most primes of…
Liftable groups, negligible cohomology and Heisenberg representations
Chandrashekhar B. Khare, Michael Larsen
We consider lifting of mod p representations to mod p^2 representations in the setting of representations of (i) finite groups; (ii) absolute Galois groups of abstract fields; and…
Multiplicative Series, Modular Forms, and Mandelbrot Polynomials
Michael Larsen
We say a power series is multiplicative if the function () is so. In this paper, we consider multiplicative power series …
Abelian Varieties and Finitely Generated Galois Groups
Bo-Hae Im, Michael Larsen
This paper surveys the methods that have been used to attack the conjecture, still open, that an abelian variety over a characteristic field with finitely generated Galois grou…
Polynomial Parametrization for over Quadratic Number Rings
Michael Larsen, Dong Quan Ngoc Nguyen
If is the ring of integers of a number field, then there exists a polynomial parametrization of the set , i.e., an element $A \in \text{SL}_2(\mathbb{Z}[x_1,\ld…
Waring's problem for rational functions in one variable
Bo-Hae Im, Michael Larsen
Let be a non-constant rational function. We consider "Waring's Problem for ," i.e., whether every element of $\bbq$ can be written as a bounded sum of el…