Add to ORKGWe prove a highly uniform version of the prime number theorem for a certain class of $L$-functions. The range of $x$ depends polynomially on the analytic conductor, and the error term is expressed in terms of an optimization problem depending explicitly on the available zero-free region. The class contains the Rankin-Selberg $L$-function $L(s,\pi \times \pi')$ associated to cuspidal automorphic representations $\pi$ and $\pi'$ of $\mathrm{GL}_{m}$ and $\mathrm{GL}_{m'}$, respectively. Our main result implies the first uniform prime number theorems for such $L$-functions (with analytic conductor uniformity) in complete generality.Comment: 14 page
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We prove that the error in the prime number theorem can be quantitatively improved beyond the Rieman...
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In the general framework of the Selberg class of L-functions we prove that the prime number theorem ...
This dissertation contributes to the analytic theory of automorphic L-functions. We prove an appro...
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Let $M$ be a squarefree positive integer and $P$ a prime number coprime to $M$ such that $P \sim M^{...
To all the people that encouraged me to study mathematics and all the people I’ve met through these ...
We establish zero-free regions tapering as an inverse power of the analytic conductor for Rankin-Sel...
We investigate properties of prime numbers and L-functions, and interactions between these two topic...
In this paper we give effective estimates for some classical arithmetic functions defined over prime...
We study certain aspects of the Selberg sieve, in particular when sifting by rather thin sets of pri...
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Three proofs of the prime number theorem are presented. The rst is a heavily analytic proof based o...
Abstract. We prove a coarse lower bound for L-functions of Langlands-Shahidi type of generic cuspida...
Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that...
We prove that the error in the prime number theorem can be quantitatively improved beyond the Rieman...
AbstractIn this paper we obtain a full asymptotic expansion of the archimedean contribution to the L...
In the general framework of the Selberg class of L-functions we prove that the prime number theorem ...
This dissertation contributes to the analytic theory of automorphic L-functions. We prove an appro...
The nonvanishing of Hecke Z-functions at the line Re (s) = 1 has proved to be useful in the theory ...
Let $M$ be a squarefree positive integer and $P$ a prime number coprime to $M$ such that $P \sim M^{...
To all the people that encouraged me to study mathematics and all the people I’ve met through these ...
We establish zero-free regions tapering as an inverse power of the analytic conductor for Rankin-Sel...
We investigate properties of prime numbers and L-functions, and interactions between these two topic...
In this paper we give effective estimates for some classical arithmetic functions defined over prime...
We study certain aspects of the Selberg sieve, in particular when sifting by rather thin sets of pri...
We give a Burgess-like subconvex bound for $L(s, \pi \otimes \chi)$ in terms of the analytical condu...
Three proofs of the prime number theorem are presented. The rst is a heavily analytic proof based o...
Abstract. We prove a coarse lower bound for L-functions of Langlands-Shahidi type of generic cuspida...
Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that...
We prove that the error in the prime number theorem can be quantitatively improved beyond the Rieman...
AbstractIn this paper we obtain a full asymptotic expansion of the archimedean contribution to the L...