• Corpus ID: 232092509

A zero density estimate and fractional imaginary parts of zeros for $\mathrm{GL}_2$ $L$-functions

@inproceedings{Beckwith2021AZD,
  title={A zero density estimate and fractional imaginary parts of zeros for \$\mathrm\{GL\}\_2\$ \$L\$-functions},
  author={Olivia Beckwith and Di Liu and Jesse Thorner and Alexandru Zaharescu},
  year={2021}
}
We prove an analogue of Selberg’s zero density estimate for ζ(s) that holds for any GL2 L-function. We use this estimate to study the distribution of the vector of fractional parts of γα, where α ∈ R is fixed and γ varies over the imaginary parts of the nontrivial zeros of a GL2 L-function. 

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References

SHOWING 1-10 OF 38 REFERENCES
FUNCTORIALITY FOR THE EXTERIOR SQUARE OF GL4 AND THE SYMMETRIC FOURTH OF GL2
Let ∧ : GLn(C) −→ GLN (C), where N = n(n−1) 2 , be the map given by the exterior square. Then Langlands’ functoriality predicts that there is a map from cuspidal representations of GLn to automorphic
The web of modularity : arithmetic of the coefficients of modular forms and q-series
Basic facts Integer weight modular forms Half-integral weight modular forms Product expansions of modular forms on $\mathrm{SL}_2(\mathbb{Z})$ Partitions Weierstrass points on modular curves Traces
Races with imaginary parts of zeros of the Riemann zeta function and Dirichlet L-functions
Abstract In this paper, we introduce a new type of race. We consider two Dirichlet L-functions L ( s , χ 1 ) , L ( s , χ 2 ) , an α ∈ R n , a test function h defined on T n and compare the sums ∑ − T
Zeros of GL2 𝐿-functions on the critical line
Abstract We use Levinson’s method and the work of Blomer and Harcos on the GL2\mathrm{GL}_{2} shifted convolution problem to prove that at least 6.96 % of the nontrivial zeros of the 𝐿-function of 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
Exponential sums with multiplicative coefficients without the Ramanujan conjecture
We study the exponential sum involving multiplicative function f under milder conditions on the range of f , which generalizes the work of Montgomery and Vaughan. As an application, we prove
L-function c++ class library and, the command line program lcalc, https: //github.com/agrawroh/l-calc, 2014, [Online; accessed 29-August-2020
  • 2020
Zeros of GL2 L-functions on the critical line, Forum Math
  • 2020
Extreme biases in prime number races with many contestants
We continue to investigate the race between prime numbers in many residue classes modulo q, assuming the standard conjectures GRH and LI. We show that provided $$n/\log q \rightarrow \infty
On the Chebotarev–Sato–Tate phenomenon
Abstract We study the Chebotarev–Sato–Tate phenomenon that concerns the distribution of Artin symbols and Frobenius angles. From the recent work of Barnet-Lamb et al., we derive some unconditional
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