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Mean value estimates for exponential sums
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This article is published in Archiv der Mathematik.The article was published on 1990-09-01. It has received 19 citations till now. The article focuses on the topics: Exponentially modified Gaussian distribution & Natural exponential family.read more
Citations
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On the divisor function and the Riemann zeta-function in short intervals
TL;DR: In this paper, asymptotic formulas for the above integrals with biquadrates instead of square were obtained for the case where Δ(x) is the error term in the classical divisor problem.
Book ChapterDOI
Coxeter Transformations associated with Finite Dimensional Algebras
TL;DR: In this article, the authors deal with the ramifications of the Coxeter transformation in finite dimensional algebra and stress its homological nature and the computational aspects with a focus on hereditary and canonical algebras.
Journal ArticleDOI
The Mellin transform of powers of the zeta-function
TL;DR: One of the basic properties of Mellin transforms is the inversion formula 1 2 {f(x + 0) + f(x 0)} = 1 2i ( ) F (s)x s ds = 1.2i lim T!1 +iT.
Book
Lectures on Mean Values of the Riemann Zeta Function
TL;DR: In this paper, an advanced text on the Riemann zeta function, a continuation of the author's earlier book, presents the most recent results on mean values, and an especially detailed discussion is given of the second and the fourth moment, and the latter is studied by the use of spectral theory, one of the most powerful methods used in analytic number theory.
Posted Content
The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound.
Ian Petrow,Matthew P. Young +1 more
TL;DR: In this paper, a Lindelof-on-average upper bound for the fourth moment of Dirichlet $L$-functions of conductor $q$ along a coset of the subgroup of characters modulo $d$ was established.
References
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Book
Topics in Multiplicative Number Theory
TL;DR: In this paper, the large sieve and the large moduli of L-functions have been studied in the context of additive prime number theory and mean value theorem of Barban.
Journal ArticleDOI
Exponential sums and the Riemann zeta function v
TL;DR: In this article, an axiomatised version of the Bombieri?Iwaniec method has been proposed, where an upper bound for the number of integer points close to a plane curve gives a bound in the Second Spacing Problem, and a small improvement in the bound for $S$.
Journal ArticleDOI
The square mean of Dirichlet series associated with cusp forms
TL;DR: The Dirichlet series is convergent for σ > ½(k + 1) as discussed by the authors, where σ is the integral weight of the full modular group and k is a constant.
Book
Lectures on a Method in the Theory of Exponential Sums
TL;DR: In this article, the authors present a lecture on the transformation of Dirichlet polynomials and their applications in analytic number theory, and the main results of these notes are established in Chapter III and some applications are given in Chapter IV.
Related Papers (5)
Mean value estimates for exponential sums and L-functions: a spectral theoretic approach.
Yoichi Motohashi,Matti Jutila +1 more