7 citations · 11 across the 13 of their papers we have counts for
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A note on the invariants of the -functions
Jerzy Kaczorowski, Alberto Perelli
We explain the exact meaning of a statement we made in a previous paper on invariants, namely that a complex-valued function of the data of the functional equation of an -functi…
Multiple standard twists of -functions
Jerzy Kaczorowski, Alberto Perelli
The standard twist of -functions plays a fundamental role in the Selberg class theory. It is defined as an absolutely convergent Dirichlet series and admits meromorphic continua…
-functions of degree and conductor : underlying ideas and a generalisation
Jerzy Kaczorowski, Alberto Perelli
We present a streamlined account of a recent theorem on the classification of the -functions of degree 2 and conductor 1 from the extended Selberg class. We also present a more…
On the sign changes of
Maciej Grześkowiak, Jerzy Kaczorowski, Łukasz Pańkowski +1
We improve the lower bound for , the number of sign changes of the error term in the Prime Number Theorem in the interval for large . We show that \[ \lim…
On the invariants of L-functions of degree 2, I: twisted degree and internal shift
J. Kaczorowski, A. Perelli
This is the first part of a series of papers where the behaviour of the invariants under twist by Dirichlet characters is studied for -functions of degree 2. Here we show, under…
Twists by Dirichlet characters and polynomial Euler products of L-functions, II
J. Kaczorowski, A. Perelli
In a previous paper we proved that if an -function from the Selberg class has degree , its conductor is a prime number and is weakly twist-regular at all primes…
Twists by Dirichlet characters and polynomial Euler products of L-functions
J. Kaczorowski, A. Perelli
We prove that suitable properties of the twists by Dirichlet characters of an L-function of degree 2 imply that its Euler product is of polynomial type.
Classification of L-functions of degree 2 and conductor 1
J. Kaczorowski, A. Perelli
We give a full description of the functions of degree 2 and conductor 1 in the general framework of the extended Selberg class. This is performed by means of a new numerical in…
On the standard twist of the L-functions of half-integral weight cusp forms
J. Kaczorowski, A. Perelli
The standard twist of -functions in the Selberg class has several interesting properties and plays a central role in the Selberg class theory. It is therefore na…
Twists and resonance of L-functions, II
J. Kaczorowski, A. Perelli
We continue our investigations of the analytic properties of nonlinear twists of L-functions developed in [4],[5] and [7]. Given an L-function of degree d, we first extend the tran…
Some remarks on the convergence of the Dirichlet series of L-functions and related questions
J. Kaczorowski, A. Perelli
First we show that the abscissae of uniform and absolute convergence of Dirichlet series coincide in the case of -functions from the Selberg class . We also study t…
Twists and resonance of L-functions, I
J. Kaczorowski, A. Perelli
We obtain the basic analytic properties, i.e. meromorphic continuation, polar structure and bounds for the order of growth, of all the nonlinear twists with exponents of…
Twists, Euler products and a converse theorem for -functions of degree 2 in the Selberg class
J. Kaczorowski, A. Perelli
We prove a general result relating the shape of the Euler product of an -function to the analytic properties of certain linear twists of the -function itself. Then, by a shar…