3 papers
math.NT2026
Reciprocity for GL(2) L-functions twisted by Dirichlet characters
Agniva Dasgupta, Rizwanur Khan, Ze Sen Tang
A formula connecting a moment of L-functions and a dual moment in a way that interchanges the roles of certain key parameters on both sides is known as a reciprocity relation. We e…
math.NT2025
Upper bounds for analytic ranks of elliptic curves over cyclotomic fields
Agniva Dasgupta, Rizwanur Khan
Let be an elliptic curve defined over . We show that the analytic rank of over the cyclotomic extension is bounded above by $q^{45/52+\…
math.NT2024
The fourth moment of truncated Eisenstein series
Goran DjankoviÄ, Rizwanur Khan
We obtain an asymptotic for the fourth moment of truncated Eisenstein series of large Laplacian eigenvalue, verifying for the first time that the main term corresponds to Gaussian…