Frobenius Distributions in GL2-Extensions

  title={Frobenius Distributions in GL2-Extensions},
  author={Serge Lang and Hale F. Trotter},


Let f be a normalized Hecke eigenform of weight k ≥ 4 on Γ0(N). Let λf(n) denote the eigenvalue of the nth Hecke operator acting on f. We show that the number of n such that λf(n) takes a given value

The Lang-Trotter conjecture on average

For an elliptic curve $E$ over $\ratq$ and an integer $r$ let $\pi_E^r(x)$ be the number of primes $p\le x$ of good reduction such that the trace of the Frobenius morphism of $E/\fie_p$ equals $r$.

Bounds for the distribution of the Frobenius traces associated to a generic abelian variety

. Let g ≥ 1 be an integer and let A be an abelian variety defined over Q and of dimension g . Assume that, for each sufficiently large prime ℓ , the image of the residual modulo ℓ Galois representation

The Lang-Trotter Conjecture for the elliptic curve $y^2=x^3+Dx$

as x −→ ∞, where CE,r is a specific non-negative constant. The Hardy-Littlewood Conjecture gives a similar asymptotic formula as above for the number of primes of the form ax + bx + c. We establish a

Effective forms of the Sato–Tate conjecture

We prove effective forms of the Sato–Tate conjecture for holomorphic cuspidal newforms which improve on the author’s previous work (solo and joint with Lemke Oliver). We also prove an effective form

The square sieve and a Lang–Trotter question for generic abelian varieties

  • Sam Bloom
  • Mathematics
    Journal of Number Theory
  • 2018

Anomalous primes of the elliptic curve ED: y2*x3+D

Let D∈Z be an integer that is neither a square nor a cube in Q(−3), and let ED be the elliptic curve defined by y2=x3+D. Mazur conjectured that the number of anomalous primes less than N should be

A Chebotarev variant of the Brun-Titchmarsh theorem and bounds for the Lang-Trotter conjectures

We improve the Chebotarev variant of the Brun-Titchmarsh theorem proven by Lagarias, Montgomery, and Odlyzko using the log-free zero density estimate and zero repulsion phenomenon for Hecke

Elliptic curves with full 2-torsion and maximal adelic Galois representations

This paper obtains necessary and sufficient conditions for the associated adelic representation to be maximal and develops a battery of computationally effective tests that can be used to verify these conditions.

The average number of amicable pairs and aliquot cycles for a family of elliptic curves

Let E be an elliptic curve over Q. Silverman and Stange defined the set (p_1,...,p_L) of distinct primes to be an aliquot cycle of length L of E if each p_i is a prime of good reduction for E such



Algebraic Number Theory

This is a corrected printing of the second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary

Hecke Polynomials as Congruence ζ Functions in Elliptic Modular Case

Introduction. Notation. ? 1. Preliminaries on quadratic fields. (Prop. 1 & Corol. 1, 2. Def. 1) ? 2. Preliminaries on elliptic curves. (Th. D, Prop. 2, 2', 3, 4, 4', 5. Lemma 1, 2. Def. 2) ? 3. C


The author proves an algebraicity theorem for the periods of parabolic forms of any weight for the full modular group, gives explicit formulas for the coefficients of the forms, and constructs -adic

Courbes modulaires de genre 1

© Mémoires de la S. M. F., 1975, tous droits réservés. L’accès aux archives de la revue « Mémoires de la S. M. F. » (http:// implique l’accord

Characters of the discrete series of representations of sl(2) over a local field.

  • P. SallyJ. Shalika
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1968

Algebraic coding theory

  • E. Berlekamp
  • Computer Science
    McGraw-Hill series in systems science
  • 1968
This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering