17 citations · 27 across the 10 of their papers we have counts for
10 papers
Euclidean ideal classes in Galois number fields of odd prime degree
V. Kumar Murty, J. Sivaraman
Weinberger in 1972, proved that the ring of integers of a number field with unit rank at least is a principal ideal domain if and only if it is a Euclidean domain, provided the…
The unipotent radical of the Mumford-Tate group of a very general mixed Hodge structure with a fixed associated graded
Payman Eskandari, V. Kumar Murty
The family of all mixed Hodge structures on a given rational vector space with a fixed weight filtration and a fixed associated graded Hodge structure $Gr^…
On unipotent radicals of motivic Galois groups
Payman Eskandari, V. Kumar Murty
Let be a neutral Tannakian category over a field of characteristic zero with unit object , and equipped with a filtration similar to the weight f…
Group schemes of square free order
V. Kumar Murty, Ying Zong
Every finite flat finitely presented group scheme G of square free order over a scheme S can be written as an extension of a finite etale S-group scheme G" by a commutative finite…
Linear and algebraic independence of Generalized Euler-Briggs constants
Sanoli Gun, V. Kumar Murty, Ekata Saha
Possible transcendental nature of Euler's constant has been the focus of study for sometime now. One possible approach is to consider not in isolation, but as an element of…
The growth of fine Selmer groups
Meng Fai Lim, V. Kumar Murty
Let A be an abelian variety defined over anumber field F. In this paper, we will investigate the growth of p-rank of the fine Selmer group in three situations. In particular, in ea…
A note on diagonal and Hermitian surfaces
Ian Blake, V. Kumar Murty, Hamid Usefi
Aspects of the properties, enumeration and construction of points on diagonal and Hermitian surfaces have been considered extensively in the literature and are further considered h…
A variant of Lehmer's conjecture, II: The CM-case
Sanoli Gun, V. Kumar Murty
Let be a normalized Hecke eigenform with rational integer Fourier coefficients. It is an interesting question to know how often an integer has a factor common with the -…
Elliptic minuscule pairs and splitting abelian varieties
V. Kumar Murty, Ying Zong
We partially answer, in terms of monodromy, Murty and Patankar's question: Given an absolutely simple abelian variety over a number field, does it have simple specializations at a…
The fundamental group of reductive Borel-Serre and Satake compactifications
Lizhen Ji, V. Kumar Murty, Leslie Saper +1
Let be an almost simple, simply connected algebraic group defined over a number field , and let be a finite set of places of including all infinite places. Let b…