9 citations · 39 across the 15 of their papers we have counts for
16 papers
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 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.
An extension of the Bourgain-Sarnak-Ziegler theorem with modular applications
Mattia Cafferata, Alberto Perelli, Alessandro Zaccagnini
We prove an extension of the Bourgain-Sarnak-Ziegler theorem and then apply it to bound certain polynomial exponential sums with modular coefficients.
A spectral universality theorem for Maass -functions
Giacomo Cherubini, Alberto Perelli
We show that for a positive proportion of Laplace eigenvalues the associated Hecke-Maass -functions approximate with arbitrary precision any target function $f(…
A rigidity theorem for translates of uniformly convergent Dirichlet series
A. Perelli, M. Righetti
It is well known that the Riemann zeta function, as well as several other -functions, is universal in the strip ; this is certainly not true for . Answering a ques…
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…
Converse theorems: from the Riemann zeta function to the Selberg class
Alberto Perelli
This is an expanded version of the author's lecture at the XX Congresso U.M.I., held in Siena in September 2015. After a brief review of L-functions, we turn to the classical conve…
Primes and prime ideals in short intervals
L. Grenié, G. Molteni, A. Perelli
We prove the analog of Cramér's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in t…
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…
An extended pair-correlation conjecture and primes in short intervals
A. Languasco, A. Perelli, A. Zaccagnini
In this paper we extend the well-known investigations of Montgomery and Goldston & Montgomery, concerning the pair-correlation function and its relations with the distribution of p…
An extension of the pair-correlation conjecture and applications
Alessandro Languasco, Alberto Perelli, Alessandro Zaccagnini
We study an extension of Montgomery's pair-correlation conjecture and its relevance in some problems on the distribution of prime numbers.
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…