منابع مشابه
Generalizing the Titchmarsh Divisor Problem
Let a be a natural number different from 0. In 1963, Linnik proved the following unconditional result about the Titchmarsh divisor problem ∑ p≤x d(p− a) = cx + O ( x log log x log x ) where c is a constant dependent on a. Titchmarsh proved the above result assuming GRH for Dirichlet L-functions in 1931. We establish the following asymptotic relation: ∑ p≤x p≡a mod k d ( p− a k ) = Ckx + O ( x l...
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We describe relations between the Evans function, a modern tool in the study of stability of traveling waves and other patterns for PDEs, and the classical Weyl-Titchmarsh function for singular Sturm-Liouville differential expressions and for matrix Hamiltonian systems. Also, we discuss a related issue of approximating eigenvalue problems on the whole line by that on finite segments.
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We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl -Titchmarsh matrixvalued functions as well as a new version of the functional model in such realizations are presented. In the case of periodic Herglotz-Nevanlinna matrix-v...
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We formulate a geometric analogue of the Titchmarsh Divisor Problem in the context of abelian varieties. For any abelian variety A defined over Q, we study the asymptotic distribution of the primes of Z which split completely in the division fields of A. For all abelian varieties which contain an elliptic curve we establish an asymptotic formula for such primes under the assumption of GRH. We e...
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Let $G$ be a group and $H$ a subgroup of $G$. $H$ is said to have semi-$Pi$-property in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $Hcap T$ has $Pi$-property in $T$. In this paper, investigating on semi-$Pi$-property of subgroups, we shall obtain some new description of finite groups.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1955
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1955-0069397-1