36 citations · 80 across the 14 of their papers we have counts for
15 papers
Products of point counts of higher genus curves over finite fields
Alina Bucur, Kiran S. Kedlaya, Arshay Sheth
Let be an elliptic curve and for each prime , let denote the number of points of modulo . The original version of the conjecture of Birch and Swinnert…
Counting number fields using multiple Dirichlet series
Brandon Alberts, Alina Bucur
We provide a method for counting number fields of fixed Galois group ordered by arbitrary inertial invariants using analytic techniques from the study of multiple Dirichlet series.…
Frobenius sign separation for abelian varieties
Alina Bucur, Francesc Fité, Kiran S. Kedlaya
Let A and A' be nonzero abelian varieties defined over a number field k such that Hom(A,A')=0. Under the Generalized Riemann hypothesis for motivic L-functions attached to A and A'…
Power-saving error terms for the number of -quartic extensions over a number field ordered by discriminant
Alina Bucur, Alexandra Florea, Allechar Serrano López +1
We study the asymptotic count of dihedral quartic extensions over a fixed number field with bounded norm of the relative discriminant. The main term of this count (including a summ…
Geometric generalizations of the square sieve, with an application to cyclic covers
Alina Bucur, Alina Carmen Cojocaru, Matilde N. Lalín +1
We formulate a general problem: given projective schemes and over a global field and a -morphism from to of finite de…
Effective Sato-Tate conjecture for abelian varieties and applications
Alina Bucur, Francesc Fité, Kiran S. Kedlaya
From the generalized Riemann hypothesis for motivic L-functions, we derive an effective version of the Sato-Tate conjecture for an abelian variety A defined over a number field k w…
Traces, high powers and one level density for families of curves over finite fields
Alina Bucur, Edgar Costa, Chantal David +2
The zeta function of a curve over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix . We develop and present a new technique to…
The distribution of -points on cyclic -covers of genus
Alina Bucur, Chantal David, Brooke Feigon +4
We study fluctuations in the number of points of -cyclic covers of the projective line over the finite field when is fixed and the genus…
Statistics for biquadratic covers of the projective line over finite fields
Elisa Lorenzo, Giulio Meleleo, Piermarco Milione +1
We study the distribution of the traces of the Frobenius endomorphism of genus curves which are quartic non-cyclic covers of , as the curve var…
Statistics for ordinary Artin-Schreier covers and other -rank strata
Alina Bucur, Chantal David, Brooke Feigon +1
We study the distribution of the number of points and of the zeroes of the zeta function in different -rank strata of Artin-Schreier covers over $\F_q$ when is fixed and the…
An application of the effective Sato-Tate conjecture
Alina Bucur, Kiran S. Kedlaya
Based on the Lagarias-Odlyzko effectivization of the Chebotarev density theorem, Kumar Murty gave an effective version of the Sato-Tate conjecture for an elliptic curve conditional…
Distribution of zeta zeroes of Artin--Schreier curves
Alina Bucur, Chantal David, Brooke Feigon +2
We study the distribution of the zeroes of the zeta functions of the family of Artin-Schreier covers of the projective line over when is fixed and the genus goes…
The probability that a complete intersection is smooth
Alina Bucur, Kiran S. Kedlaya
Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is…
The fluctuations in the number of points of smooth plane curves over finite fields
Alina Bucur, Chantal David, Brooke Feigon +1
In this note, we study the fluctuations in the number of points of smooth projective plane curves over finite fields as is fixed and the genus varies. More preci…
Statistics for traces of cyclic trigonal curves over finite fields
Alina Bucur, Chantal David, Brooke Feigon +1
We study the variation of the trace of the Frobenius endomorphism associated to a cyclic trigonal curve of genus g over a field of q elements as the curve varies in an irreducible…