15 citations · 24 across the 11 of their papers we have counts for
12 papers · 1 filter
An analog of the Edwards model for Jacobians of genus 2 curves
E. Victor Flynn, Kamal Khuri-Makdisi
We give the explicit equations for a P^3 x P^3 embedding of the Jacobian of a curve of genus 2, which gives a natural analog for abelian surfaces of the Edwards curve model of elli…
Values of L-Series of Hecke Eigenforms
Kamal Khuri-Makdisi, Winfried Kohnen, Wissam Raji
We determine a formula for the average values of L-series associated to eigenforms at complex values.
Fake proofs for identities involving products of Eisenstein series
Kamal Khuri-Makdisi
In the workshop of the July 2016 Building Bridges 3 conference in Sarajevo, I presented the results from a joint article with W. Raji (Mathematische Annalen 2017, preprint arXiv:14…
Modular forms constructed from moduli of elliptic curves, with applications to explicit models of modular curves
Kamal Khuri-Makdisi
These are the lecture notes from my portion of a mini-course for the summer school "Building Bridges 3" that was held in Sarajevo during July 2016. My lectures covered the Katz def…
Periods of modular forms and identities between Eisenstein series
Kamal Khuri-Makdisi, Wissam Raji
Borisov and Gunnells observed in 2001 that certain linear relations between products of two holomorphic weight 1 Eisenstein series had the same structure as the relations between p…
On Jacobian group arithmetic for typical divisors on curves
Kamal Khuri-Makdisi
In a previous joint article with F. Abu Salem, we gave efficient algorithms for Jacobian group arithmetic of "typical" divisor classes on C_{3,4} curves, improving on similar resul…
Moduli interpretation of Eisenstein series
Kamal Khuri-Makdisi
Let L >= 3. Using the moduli interpretation, we define certain elliptic modular forms of level Gamma(L) over any field k where 6L is invertible and k contains the Lth roots of unit…
On the maps from X(4p) to X(4)
Samar Jaafar, Kamal Khuri-Makdisi
We study pullbacks of modular forms of weight 1 from the modular curve X(4) to the modular curve X(4p), where p is an odd prime. We find the extent to which such modular forms sepa…
Generating functions for Hecke operators
Hala Hajj Shehadeh, Samar Jaafar, Kamal Khuri-Makdisi
Fix a prime N, and consider the action of the Hecke operator T_N on the space M_k(SL(2,Z)) of modular forms of full level and varying weight k. The coefficients of the matrix of T_…
Fast Jacobian group operations for C_{3,4} curves over a large finite field
Fatima K. Abu Salem, Kamal Khuri-Makdisi
Let C be an arbitrary smooth algebraic curve of genus g over a large finite field K. We revisit fast addition algorithms in the Jacobian of C due to Khuri-Makdisi (math.NT/0409209,…
Asymptotically fast group operations on Jacobians of general curves
Kamal Khuri-Makdisi
Let be a curve of genus over a field . We describe probabilistic algorithms for addition and inversion of the classes of rational divisors in the Jacobian of . After…
Linear algebra algorithms for divisors on an algebraic curve
Kamal Khuri-Makdisi
We use an embedding of the symmetric th power of any algebraic curve of genus into a Grassmannian space to give algorithms for working with divisors on , using only l…