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Creators/Authors contains: "BUCUR, ALINA"

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  1. ; ; ; (, Research Directions in Number Theory Women in Numbers V)
    Accepted Manuscript Full Text Available
  2. ; ; (, Journal of the European Mathematical Society)
    Full Text Available 
  3. (, Panoramas et synthèses Société mathématique de France)
    Bassa, Alp; Lorenzo_Garcia, Elisa; Ritzenthaler, Christophe (Ed.)
    Accepted Manuscript Full Text Available
  4. ; ; ; (, Mathematika)
    Abstract We formulate a general problem: Given projective schemes and over a global fieldKand aK‐morphism η from to of finite degree, how many points in of height at mostBhave a pre‐image under η in ? This problem is inspired by a well‐known conjecture of Serre on quantitative upper bounds for the number of points of bounded height on an irreducible projective variety defined over a number field. We give a nontrivial answer to the general problem when and is a prime degree cyclic cover of . Our tool is a new geometric sieve, which generalizes the polynomial sieve to a geometric setting over global function fields. 
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  5. ; ; ; ; (, Mathematical Proceedings of the Cambridge Philosophical Society)
    Abstract The zeta function of a curve C over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix Θ C . We develop and present a new technique to compute the expected value of tr(Θ C n ) for various moduli spaces of curves of genus g over a fixed finite field in the limit as g is large, generalising and extending the work of Rudnick [ Rud10 ] and Chinis [ Chi16 ]. This is achieved by using function field zeta functions, explicit formulae, and the densities of prime polynomials with prescribed ramification types at certain places as given in [ BDF + 16 ] and [ Zha ]. We extend [ BDF + 16 ] by describing explicit dependence on the place and give an explicit proof of the Lindelöf bound for function field Dirichlet L -functions L (1/2 + it , χ). As applications, we compute the one-level density for hyperelliptic curves, cyclic ℓ-covers, and cubic non-Galois covers. 
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