21 citations · 56 across the 7 of their papers we have counts for
9 papers
Counting abelian varieties over finite fields via Frobenius densities
Jeff Achter, Salim Ali Altug, Luis Garcia +3
Let be a principally polarized abelian variety over a finite field with commutative endomorphism ring; further suppose that either is ordinary or the field is prime. Mo…
Hard isogeny problems over RSA moduli and groups with infeasible inversion
Salim Ali Altug, Yilei Chen
We initiate the study of computational problems on elliptic curve isogeny graphs defined over RSA moduli. We conjecture that several variants of the neighbor-search problem over th…
The number of quartic -fields ordered by conductor
Salim Ali Altug, Arul Shankar, Ila Varma +1
We consider families of number fields of degree 4 whose normal closures over have Galois group isomorphic to , the symmetries of a square. To any such field ,…
Beyond Endoscopy via the trace formula - III: The standard representation
Salim Ali Altug
We finalize the analysis of the trace formula initiated in \cite{Altug:2015aa} and developed in \cite{Altug:2015ab}, and calculate the asymptotic expansion of the beyond endoscopic…
Elliptic curves, random matrices and orbital integrals
Jeff Achter, Julia Gordon, Salim Ali Altug
An isogeny class of elliptic curves over a finite field is determined by a quadratic Weil polynomial. Gekeler has given a product formula, in terms of congruence considerations inv…
Beyond Endoscopy via the Trace Formula-I: Poisson Summation and Contributions of Special Representations
Salim Ali Altug
With analytic applications in mind, in particular Beyond Endoscopy ([13]), we initiate the study of the elliptic part of the trace formula. Incorporating the approximate functional…
Beyond Endoscopy via the trace formula - II: Asymptotic expansions of Fourier transforms and bounds towards the Ramanujan conjecture
Salim Ali Altug
We continue the analysis of the elliptic part of the trace formula initiated in \cite{Altug:2015aa}. In that reference Poisson summation was applied to the elliptic part and the do…
A Recursion Formula for Moments of Derivatives of Random Matrix Polynomials
S. Ali Altug, Sandro Bettin, Ian Petrow +2
We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp(2N), SO(2N) and O^-(2N). These averages are used to predict…
Metaplectic Ramanujan conjecture over function fields with applications to quadratic forms
S. Ali Altug, Jacob Tsimerman
We formulate and prove the analogue of the Ramanujan Conjectures for modular forms of half-integral weight subject to some ramification restriction in the setting of a polynomial r…