18 citations · 24 across the 7 of their papers we have counts for
8 papers
Non-ordinary curves with a Prym variety of low -rank
Turku Ozlum Celik, Yara Elias, Burcin Gunes +4
If is an unramified double cover of a smooth curve of genus , then the Prym variety is a principally polarized abelian variety of dimension . When is…
Heights of CM cycles and derivatives of L-series
Yara Elias, Tian An Wong
We extend the work of S. Zhang and Yuan-Zhang-Zhang to obtain a Gross-Zagier formula for modular forms of even weight in terms of an arithmetic intersection pairing of CM-cycles on…
CM cycles on Kuga-Sato varieties over Shimura curves and Selmer groups
Yara Elias, Carlos de Vera-Piquero
Given a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga-S…
On Generalized Addition Chains
Yara Elias, Pierre McKenzie
Given integers d >= 1, and g >= 2, a g-addition chain for d is a sequence of integers a_0=1, a_1, a_2,..., a_{r-1}, a_r=d where a_i=a_{j_1}+a_{j_2}+...+a_{j_k}, with 2 =< k =< g, a…
Ring-LWE Cryptography for the Number Theorist
Yara Elias, Kristin E. Lauter, Ekin Ozman +1
In this paper, we survey the status of attacks on the ring and polynomial learning with errors problems (RLWE and PLWE). Recent work on the security of these problems [Eisenträger-…
On the Selmer group attached to a modular form and an algebraic Hecke character
Yara Elias
We construct an Euler system of generalized Heegner cycles to bound the Selmer group associated to a modular form and an algebraic Hecke character. The main argument is based on Ko…
Kolyvagin's method for Chow groups of Kuga-Sato varieties over ring class fields
Yara Elias
We use an Euler system of Heegner cycles to bound the Selmer group associated to a modular form of higher even weight twisted by a ring class character. This is an extension of Nek…
Provably weak instances of Ring-LWE
Yara Elias, Kristin E. Lauter, Ekin Ozman +1
The ring and polynomial learning with errors problems (Ring-LWE and Poly-LWE) have been proposed as hard problems to form the basis for cryptosystems, and various security reductio…