1,721,037 research outputs found
Analytic Number Theory
No full textLectures given by J. B. Friedlander, D. R. Heath-Brown, H. Iwaniec, J. Kaczorowski at a C.I.M.E. Summer School held in Cetraro, Italy. Editors: A. Perelli and C. Viola. Springer Lecture Notes in Mathematics vol. 1891
Zeta functions of finite fields and the Selberg class
No full textWe analyze the relations between the zeta functions of smooth projective varieties over finite fields and the functions of degree from the extended Selberg class. In particular, denoting such functions by , we first describe how to associate suitable local -functions from to the varieties over a finite field. Then we show that, in a suitable sense and under a certain hypothesis, is generated by the local -functions coming from curves
On the standard twist of the L-functions of half-integral weight cusp forms
No full textThe 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 natural to study its finer analytic properties, for example the functional equation. Here we deal with a special case, where satisfies a functional equation with the same -factor of the -functions associated with the cusp forms of half-integral weight; for simplicity we present our results directly for such -functions. We show that the standard twist satisfies a functional equation reflecting to , whose shape is not far from a Riemann-type functional equation of degree 2 and may be regarded as a degree 2 analog of the Hurwitz-Lerch functional equation. We also deduce some result on the growth on vertical strips and on the distribution of zeros of
On the Rankin-Selberg convolution of degree functions from the extended Selberg class
No full textLet be a function of degree from the extended Selberg class. Assuming certain bounds for the shifted convolution sums associated with , we prove that the Rankin-Selberg convolution has holomorphic continuation to the half-plane si> heta apart from a simple pole at , where 1/2< heta<1 depends on the above mentioned bounds
The exceptional set for the number of primes in short intervals
Full text linkAbstractWe investigate the exceptional set Eδ(X, h) associated with the asymptotic formula for the number of primes in short intervals; see Section 1 for the definition. We first obtain two results about the basic structure of this set, proving the inertia and decrease properties; see Theorem 1. Then we turn to estimates for the size of Eδ(X, h), showing that non-trivial bounds for |Eδ(X, h)| can be obtained when h(x)=xθ and 1/6<θ<7/12; see Theorem 2
An extension of the Bourgain-Sarnak-Ziegler theorem with modular applications
No full textWe first prove an extension of the Bourgain-Sarnak-Ziegler theorem, relaxing some conditions and giving quantitative estimates. Then we apply our extension to bound certain exponential sums, where the coefficients come from modular forms and the exponential involves polynomial sequences of any degre
Explicit formulae for averages of Goldbach representations
No full textWe prove an explicit formula, analogous to the classical explicit formula for , for the Cesaro-Riesz mean of any order k>0 of the number of representations of as a sum of two primes. Our approach is based on a double Mellin transform and the analytic continuation of certain functions arising therein
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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