12 citations · 23 across the 6 of their papers we have counts for
7 papers
On the structure of locally potentially equivalent Galois representations
Vijay M. Patankar, C. S. Rajan
Suppose are two -adic Galois representations of the absolute Galois group of a number field, such that the algebraic monodromy group of one of the representations…
Applications of the square sieve to a conjecture of Lang and Trotter for a pair of elliptic curves over the rationals
Stephan Baier, Vijay M. Patankar
Let be an elliptic curve over . Let be a prime of good reduction for . Then, for a prime , the Frobenius automorphism associated to (unique…
Distinguishing Galois representations by their normalized traces
Vijay M. Patankar, C. S. Rajan
Suppose \( ρ_1 \) and \( ρ_2 \) are two pure Galois representations of the absolute Galois group of a number field of weights \( k_1 \) and \( k_2 \) respectively, having equal…
Locally potentially equivalent two dimensional Galois representations and Frobenius fields of elliptic curves
Manisha Kulkarni, Vijay M. Patankar, C. S. Rajan
We show that a two dimensional -adic representation of the absolute Galois group of a number field which is locally potentially equivalent to a --adic represent…
Tate Cycles on Abelian Varieties with Complex Multiplication
V. Kumar Murty, Vijay M. Patankar
We consider Tate cycles on an Abelian variety defined over a sufficiently large number field and having complex multiplication. We show that there is an effective bound $C…
Locally potentially equivalent Galois representations
Vijay M. Patankar, C. S. Rajan
We show that if two continuous semi-simple \(\ell \)-adic Galois representations are locally potentially equivalent at a sufficiently large set of places then they are globaly pote…