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pro vyhledávání: '"Kaczorowski J"'
Autor:
Kaczorowski, J., Perelli, A.
This is the first part of a series of papers where the behaviour of the invariants under twist by Dirichlet characters is studied for $L$-functions of degree 2. Here we show, under suitable conditions, that degree and internal shift remain unchanged
Externí odkaz:
http://arxiv.org/abs/2405.03186
Autor:
Kaczorowski, J., Perelli, A.
In a previous paper we proved that if an $L$-function $F$ from the Selberg class has degree $2$, its conductor $q_F$ is a prime number and $F$ is weakly twist-regular at all primes $p\neq q_F$, then $F$ has a polynomial Euler product. In this paper w
Externí odkaz:
http://arxiv.org/abs/2303.02420
Autor:
Kaczorowski, J., Perelli, A.
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.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/2303.02417
In this paper we study the forbidden values of the conductor $q$ of the $L$-functions of degree 2 in the extended Selberg class by a novel technique, linking the problem to certain continued fractions and to their weight $w_q$. Our basic result state
Externí odkaz:
http://arxiv.org/abs/2208.12947
Autor:
Kaczorowski, J., Perelli, A.
We give a full description of the functions $F$ of degree 2 and conductor 1 in the general framework of the extended Selberg class. This is performed by means of a new numerical invariant $\chi_F$, which is easily computed from the data of the functi
Externí odkaz:
http://arxiv.org/abs/2009.12329
Autor:
Kaczorowski, J., Perelli, A.
Publikováno v:
Acta Arith. 201 (2021), 281-328
The analytic properties of the standard twist $F(s,\alpha)$, where $F(s)$ belongs to a wide class of $L$-functions, are of prime importance in describing the structure of the Selberg class. In this paper we present a deeper study of such properties.
Externí odkaz:
http://arxiv.org/abs/1911.10497
Publikováno v:
Trans. Amer. Math. Soc. 372 (2019), 6981-6999
We prove an explicit formula, analogous to the classical explicit formula for $\psi(x)$, for the Ces\`aro-Riesz mean of any order $k>0$ of the number of representations of $n$ as a sum of two primes. Our approach is based on a double Mellin transform
Externí odkaz:
http://arxiv.org/abs/1712.00737
Autor:
Kaczorowski, J., Perelli, A.
The standard twist $F(s,\alpha)$ of $L$-functions $F(s)$ in the Selberg class has several interesting properties and plays a central role in the Selberg class theory. It is therefore natural to study its finer analytic properties, for example the fun
Externí odkaz:
http://arxiv.org/abs/1701.03929
Akademický článek
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Autor:
Kaczorowski, J., Perelli, A.
Publikováno v:
Int. Math. Res. Notices (2016), 7637-7670
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 transformation formula in [5], relating a twist with leading exponent > 1/
Externí odkaz:
http://arxiv.org/abs/1507.07177