31 citations · 167 across the 19 of their papers we have counts for
19 papers
An explicit version of Bombieri's log-free density estimate and Sárközy's theorem for shifted primes
Jesse Thorner, Asif Zaman
We make explicit Bombieri's refinement of Gallagher's log-free "large sieve density estimate near " for Dirichlet -functions. We use this estimate and recent work of Green…
Refinements to the prime number theorem for arithmetic progressions
Jesse Thorner, Asif Zaman
We prove a version of the prime number theorem for arithmetic progressions that is uniform enough to deduce the Siegel-Walfisz theorem, Hoheisel's asymptotic for intervals of lengt…
A conjectural asymptotic formula for multiplicative chaos in number theory
Daksh Aggarwal, Unique Subedi, William Verreault +2
We investigate a special sequence of random variables defined by an exponential power series with independent standard complex Gaussians . Introduced by H…
A model problem for multiplicative chaos in number theory
Kannan Soundararajan, Asif Zaman
Resolving a conjecture of Helson, Harper recently established that partial sums of random multiplicative functions typically exhibit more than square-root cancellation. Harper's wo…
Sums of random multiplicative functions over function fields with few irreducible factors
Daksh Aggarwal, Unique Subedi, William Verreault +2
We establish a normal approximation for the limiting distribution of partial sums of random Rademacher multiplicative functions over function fields, provided the number of irreduc…
An approximate form of Artin's holomorphy conjecture and non-vanishing of Artin -functions
Robert J. Lemke Oliver, Jesse Thorner, Asif Zaman
Let be a number field and be a finite group. Let be the family of number fields with absolute discriminant at most such that i…
A zero density estimate for Dedekind zeta functions
Jesse Thorner, Asif Zaman
Given a nontrivial finite group , we prove the first zero density estimate for families of Dedekind zeta functions associated to Galois extensions with $\mathrm{G…
An unconditional large sieve
Jesse Thorner, Asif Zaman
Let be the set of all cuspidal automorphic representations of over a number field with unitary central character. We prove two unconditional la…
Zeros of Rankin-Selberg -functions at the edge of the critical strip
Farrell Brumley, Jesse Thorner, Asif Zaman
Let and be unitary cuspidal automorphic representations. We prove log-free zero density estimates for Rankin-Selberg -functions of the form , where $π…
A unified and improved Chebotarev density theorem
Jesse Thorner, Asif Zaman
We establish an unconditional effective Chebotarev density theorem that improves uniformly over the well-known result of Lagarias and Odlyzko. As a consequence, we give a new asymp…
Primes represented by positive definite binary quadratic forms
Asif Zaman
Let be a primitive positive definite integral binary quadratic form of discriminant and let be the number of primes up to which are represented by . We pro…
The Density of Numbers Represented by Diagonal Forms of Large Degree
Brandon Hanson, Asif Zaman
Let be a fixed positive integer and be arbitrary. We show that, on average over , the density of numbers represented by the degree …
The least unramified prime which does not split completely
Asif Zaman
Let be a finite extension of number fields of degree . We establish effective field-uniform unconditional upper bounds for the least norm of a prime ideal of wh…
A Chebotarev variant of the Brun-Titchmarsh theorem and bounds for the Lang-Trotter conjectures
Jesse Thorner, Asif Zaman
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…
An explicit bound for the least prime ideal in the Chebotarev density theorem
Jesse Thorner, Asif Zaman
We prove an explicit version of Weiss' bound on the least norm of a prime ideal in the Chebotarev density theorem, which is itself a significant improvement on the work of Lagarias…
Explicit results on the distribution of zeros of Hecke -functions
Jesse Thorner, Asif Zaman
We prove an explicit log-free zero density estimate and an explicit version of the zero-repulsion phenomenon of Deuring and Heilbronn for Hecke -functions. In forthcoming work o…
Bounding the least prime ideal in the Chebotarev Density Theorem
Asif Zaman
Let be a finite Galois extension of the number field . We unconditionally bound the least prime ideal of occurring in the Chebotarev Density Theorem as a power of the di…
On the least prime ideal and Siegel zeros
Asif Zaman
Let be a number field, be an integral ideal, and be the associated ray class group. Suppose possesses a r…
Explicit estimates for the zeros of Hecke -functions
Asif Zaman
Let be a number field and, for an integral ideal of , let be a character of the narrow ray class group modulo . We establish various new and…