GLORIA

GEOMAR Library Ocean Research Information Access

X

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Online Resource  (44)
  • Ramachandra, K  (44)
  • 1
    Online Resource
    Online Resource
    A remark on a theorem of A. E. Ingham.
    Centre pour la Communication Scientifique Directe (CCSD) ; 2006
    In:  Hardy-Ramanujan Journal Vol. Volume 29 - 2006 ( 2006-01-01)
    Details
    In: Hardy-Ramanujan Journal, Centre pour la Communication Scientifique Directe (CCSD), Vol. Volume 29 - 2006 ( 2006-01-01)
    Abstract: Referring to a theorem of A. E. Ingham, that for all $N\geq N_0$ (an absolute constant), the inequality $N^3\leq p\leq(N+1)^3$ is solvable in a prime $p$, we point out in this paper that it is implicit that he has actually proved that $\pi(x+h)-\pi(x) \sim h(\log x)^{-1}$ where $h=x^c$ and $c ( 〉 \frac{5}{8})$ is any constant. Further, we point out that even this stronger form can be proved without using the functional equation of $\zeta(s)$.
    Type of Medium: Online Resource
    ISSN: 2804-7370
    URL: Journal
    URL: Article
    DOI: 10.46298/journals/hrj
    DOI: 10.46298/hrj.2006.155
    Language: English
    Publisher: Centre pour la Communication Scientifique Directe (CCSD)
    Publication Date: 2006
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 2
    Online Resource
    Online Resource
    Ramanujan's lattice point problem, prime number theory and other remarks.
    Centre pour la Communication Scientifique Directe (CCSD) ; 1996
    In:  Hardy-Ramanujan Journal Vol. Volume 19 - 1996 ( 1996-01-01)
    Details
    In: Hardy-Ramanujan Journal, Centre pour la Communication Scientifique Directe (CCSD), Vol. Volume 19 - 1996 ( 1996-01-01)
    Abstract: This paper gives results on four diverse topics. The first result is that the error term for the number of integers $2^u3^v \le n$ is $O((\log n)^{1-\delta})$ with $\delta=(2^{40}(\log3))^{-1}$, using a theorem of A. Baker and G. W\"ustholz. The second result is an averaged explicit formula \[ \psi(x) = x-\frac{1}{T} \int_{T}^{2T} \left( \sum \limits_{|\gamma| \le \tau} \frac{x^{\rho}}{\rho} \right) \ d\tau + O \left( \frac{\log x}{\log \frac{x}{T}}\cdot \frac{x}{T} \right) \] for $x \gg T \gg 1$. It then follows, by the Riemann hypothesis, that $\psi (x+h)-\psi (x)= h+ O \left ( h \lambda^{1/2} \right )$ if $h=\lambda x^{1/2} \log x$. The third theme tightens the $\log$ powers in the zero density bounds of Ingham and Huxley, and gives corollaries for the mean-value of $\psi (x+h)-\psi (x)-h$. The fourth remark concerns a hypothetical improvement in the constant 2 in the Brun-Titchmarsh theorem, averaged over congruence classes, and its consequence for $L \left ( 1,\chi \right )$.
    Type of Medium: Online Resource
    ISSN: 2804-7370
    URL: Journal
    URL: Article
    DOI: 10.46298/journals/hrj
    DOI: 10.46298/hrj.1996.133
    Language: English
    Publisher: Centre pour la Communication Scientifique Directe (CCSD)
    Publication Date: 1996
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 3
    Online Resource
    Online Resource
    Remark on Factorials that are Products of Factorials
    Steklov Mathematical Institute ; 2010
    In:  Matematicheskie Zametki Vol. 88, No. 3 ( 2010), p. 350-354
    Details
    In: Matematicheskie Zametki, Steklov Mathematical Institute, Vol. 88, No. 3 ( 2010), p. 350-354
    Type of Medium: Online Resource
    ISSN: 0025-567X
    URL: Journal
    URL: Article
    DOI: 10.4213/mzm
    DOI: 10.4213/mzm8664
    Language: Russian
    Publisher: Steklov Mathematical Institute
    Publication Date: 2010
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 4
    Online Resource
    Online Resource
    Notes on the Riemann zeta-function-IV
    Centre pour la Communication Scientifique Directe (CCSD) ; 2000
    In:  Hardy-Ramanujan Journal Vol. Volume 23 - 2000 ( 2000-01-01)
    Details
    In: Hardy-Ramanujan Journal, Centre pour la Communication Scientifique Directe (CCSD), Vol. Volume 23 - 2000 ( 2000-01-01)
    Abstract: In earlier papers of this series III and IV, poles of certain meromorphic functions involving Riemann's zeta-function at shifted arguments and Dirichlet polynomials were studied. The functions in question were quotients of products of such functions, and it was shown that they have ``many'' poles. The main result in the present paper is that the same conclusion remains valid even for finite sums of functions of this type.
    Type of Medium: Online Resource
    ISSN: 2804-7370
    URL: Journal
    URL: Article
    DOI: 10.46298/journals/hrj
    DOI: 10.46298/hrj.2000.141
    Language: English
    Publisher: Centre pour la Communication Scientifique Directe (CCSD)
    Publication Date: 2000
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 5
    Online Resource
    Online Resource
    Notes on the Riemann zeta Function-III
    Centre pour la Communication Scientifique Directe (CCSD) ; 1999
    In:  Hardy-Ramanujan Journal Vol. Volume 22 - 1999 ( 1999-01-01)
    Details
    In: Hardy-Ramanujan Journal, Centre pour la Communication Scientifique Directe (CCSD), Vol. Volume 22 - 1999 ( 1999-01-01)
    Abstract: For a good Dirichlet series $F(s)$ (see Definition in \S1) which is a quotient of some products of the translates of the Riemann zeta-function, we prove that there are infinitely many poles $p_1+ip_2$ in $\Im (s) 〉 C$ for every fixed $C 〉 0$. Also, we study the gaps between the ordinates of the consecutive poles of $F(s)$.
    Type of Medium: Online Resource
    ISSN: 2804-7370
    URL: Journal
    URL: Article
    DOI: 10.46298/journals/hrj
    DOI: 10.46298/hrj.1999.139
    Language: English
    Publisher: Centre pour la Communication Scientifique Directe (CCSD)
    Publication Date: 1999
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 6
    Online Resource
    Online Resource
    On the frequency of titchmarsh’s phenomenon for ζ(s)—III
    Springer Science and Business Media LLC ; 1977
    In:  Proceedings of the Indian Academy of Sciences - Section A Vol. 86, No. 4 ( 1977-10), p. 341-351
    Details
    In: Proceedings of the Indian Academy of Sciences - Section A, Springer Science and Business Media LLC, Vol. 86, No. 4 ( 1977-10), p. 341-351
    Type of Medium: Online Resource
    ISSN: 0370-0089
    URL: Article
    DOI: 10.1007/BF03046849
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 1977
    detail.hit.zdb_id: 2064209-X
    detail.hit.zdb_id: 2081712-5
    detail.hit.zdb_id: 2099136-8
    SSG: 13
    SSG: 17,1
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 7
    Online Resource
    Online Resource
    Some remarks on the mean value of the Riemann zeta-function and other Dirichlet series 1
    Centre pour la Communication Scientifique Directe (CCSD) ; 1978
    In:  Hardy-Ramanujan Journal Vol. Volume 1 - 1978 ( 1978-01-01)
    Details
    In: Hardy-Ramanujan Journal, Centre pour la Communication Scientifique Directe (CCSD), Vol. Volume 1 - 1978 ( 1978-01-01)
    Abstract: The present paper is concerned with $\Omega$-estimates of the quantity $$(1/H)\int_{T}^{T+H}\vert(d^m/ds^m)\zeta^k(\frac{1}{2}+it)\vert dt$$ where $k$ is a positive number (not necessarily an integer), $m$ a nonnegative integer, and $(\log T)^{\delta}\leq H \leq T$, where $\delta$ is a small positive constant. The main theorems are stated for Dirichlet series satisfying certain conditions and the corollaries concerning the zeta function illustrate quite well the scope and interest of the results. %It is proved that if $2k\geq1$ and $T\geq T_0(\delta)$, then $$(1/H)\int_{T}^{T+H}\vert \zeta(\frac{1}{2}+it)\vert^{2k}dt 〉 (\log H)^{k^2}(\log\log H)^{-C}$$ and $$(1/H)\int_{T}^{T+H} \vert\zeta'(\frac{1}{2}+it)\vert dt 〉 (\log H)^{5/4}(\log\log H)^{-C},$$ where $C$ is a constant depending only on $\delta$.
    Type of Medium: Online Resource
    ISSN: 2804-7370
    URL: Journal
    URL: Article
    DOI: 10.46298/journals/hrj
    DOI: 10.46298/hrj.1978.87
    Language: English
    Publisher: Centre pour la Communication Scientifique Directe (CCSD)
    Publication Date: 1978
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 8
    Online Resource
    Online Resource
    One more proof of Siegel's theorem
    Centre pour la Communication Scientifique Directe (CCSD) ; 1980
    In:  Hardy-Ramanujan Journal Vol. Volume 3 - 1980 ( 1980-01-01)
    Details
    In: Hardy-Ramanujan Journal, Centre pour la Communication Scientifique Directe (CCSD), Vol. Volume 3 - 1980 ( 1980-01-01)
    Abstract: This paper gives a new elementary proof of the version of Siegel's theorem on $L(1,\chi)=\sum_{n=1}^{\infty}\chi(n)n^{-1}$ for a real character $\chi(\!\!\!\!\mod k)$. The main result of this paper is the theorem: If $3\leq k_1\leq k_2$ are integers, $\chi_1(\!\!\!\!\mod k_1)$ and $\chi_2(\!\!\!\!\mod k_2)$ are two real non-principal characters such that there exists an integer $n 〉 0$ for which $\chi_1(n)\cdot\chi_2(n)=-1$ and, moreover, if $L(1,\chi_1)\leq10^{-40}(\log k_1)^{-1}$, then $L(1,\chi_2) 〉 10^{-4} (\log k_2){-1}\cdot(\log k_1)^{-2}k_2^{-40000L(1,\chi_1)}$. From this the result of T. Tatuzawa on Siegel's theorem follows.
    Type of Medium: Online Resource
    ISSN: 2804-7370
    URL: Journal
    URL: Article
    DOI: 10.46298/journals/hrj
    DOI: 10.46298/hrj.1980.89
    Language: English
    Publisher: Centre pour la Communication Scientifique Directe (CCSD)
    Publication Date: 1980
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 9
    Online Resource
    Online Resource
    Addendum and corrigendum to my paper - "One more proof of Siegel's theorem"
    Centre pour la Communication Scientifique Directe (CCSD) ; 1981
    In:  Hardy-Ramanujan Journal Vol. Volume 4 - 1981 ( 1981-01-01)
    Details
    In: Hardy-Ramanujan Journal, Centre pour la Communication Scientifique Directe (CCSD), Vol. Volume 4 - 1981 ( 1981-01-01)
    Abstract: In the original paper we noticed a problem with the assertion $L(1,\chi_1)\neq0$ in Lemma 3 of Section 1. The problem is cleared up here. The assertions of the paper all remain valid.
    Type of Medium: Online Resource
    ISSN: 2804-7370
    URL: Journal
    URL: Article
    DOI: 10.46298/journals/hrj
    DOI: 10.46298/hrj.1981.94
    Language: English
    Publisher: Centre pour la Communication Scientifique Directe (CCSD)
    Publication Date: 1981
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 10
    Online Resource
    Online Resource
    Mean-value of the Riemann zeta-function and other remarks III
    Centre pour la Communication Scientifique Directe (CCSD) ; 1983
    In:  Hardy-Ramanujan Journal Vol. Volume 6 - 1983 ( 1983-01-01)
    Details
    In: Hardy-Ramanujan Journal, Centre pour la Communication Scientifique Directe (CCSD), Vol. Volume 6 - 1983 ( 1983-01-01)
    Abstract: The results given in these papers continue the theme developed in part I of this series. In Part III we prove $M(\frac{1}{2}) 〉 \!\!\! 〉 _k (\log H_0/q_n)^{k^2}$, where $p_m/q_m$ is the $m$th convergent of the continued fraction expansion of $k$, and $n$ is the unique integer such that $q_nq_{n+1}\geq \log\log H_0 〉 q_nq_{n-1}$. Section 4 of part III discusses lower bounds of mean values of Titchmarsh series.
    Type of Medium: Online Resource
    ISSN: 2804-7370
    URL: Journal
    URL: Article
    DOI: 10.46298/journals/hrj
    DOI: 10.46298/hrj.1983.96
    Language: English
    Publisher: Centre pour la Communication Scientifique Directe (CCSD)
    Publication Date: 1983
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...