Results 21 to 30 of about 3,206 (154)
Linnik’s problems and maximal entropy methods [PDF]
Monatshefte für Mathematik, 2019 We use maximal entropy methods to examine the distribution properties of primitive integer points on spheres and of CM points on the modular surface. The proofs we give are a modern and dynamical interpretation of Linnik's original ideas and follow techniques presented by Einsiedler, Lindenstrauss, Michel and Venkatesh in 2011.
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A Ces\`aro Average of Goldbach numbers [PDF]
, 2012 Let $\Lambda$ be the von Mangoldt function and $(r_G(n) = \sum_{m_1 + m_2 = n} \Lambda(m_1) \Lambda(m_2))$ be the counting function for the Goldbach numbers. Let $N \geq 2$ be an integer.
Languasco, Alessandro +1 more
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Footnote to the Titchmarsh-Linnik divisor problem [PDF]
Proceedings of the American Mathematical Society, 1967 The study of Ta(x) was initiated as long ago as 1931 by Titchmarsh [2]. Since the dispersion method is exceedingly complicated, it may be of interest to record that the theorem is a simple consequence of the recent result of Bombieri [3] on the average of the error term in the prime number theorem for arithmetic progressions.
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On pairs of equations in unlike powers of primes and powers of 2
Open Mathematics, 2017 In this paper, we obtained that when k = 455, every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of unlike powers of primes and k powers of 2.
Hu Liqun, Yang Li
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Elliptic curve variants of the least quadratic nonresidue problem and Linnik’s theorem [PDF]
International Journal of Number Theory, 2017 Let [Formula: see text] and [Formula: see text] be [Formula: see text]-nonisogenous, semistable elliptic curves over [Formula: see text], having respective conductors [Formula: see text] and [Formula: see text] and both without complex multiplication. For each prime [Formula: see text], denote by [Formula: see text] the trace of Frobenius.
Chen, Evan +2 more
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Two Linnik-type problems for automorphic L-functions [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2011 AbstractLet m ≥ 2 be an integer, and π an irreducible unitary cuspidal representation for GLm(), whose attached automorphic L-function is denoted by L(s, π). Let {λπ(n)}n=1∞ be the sequence of coefficients in the Dirichlet series expression of L(s, π) in the half-plane ℜs > 1.
JIANYA LIU, YAN QU, JIE WU
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On Linnik's theorem on Goldbach numbers in short intervals and related problems [PDF]
Annales de l'Institut Fourier, 1994 Linnik proved, assuming the Riemann Hypothesis, that for any ϵ>0, the interval [N,N+log 3+ϵ N] contains a number which is the sum of two primes, provided that N is sufficiently large. This has subsequently been improved to the same assertion being valid for the smaller gap Clog 2 N, the added new ingredient being Selberg’s estimate for the mean ...
A. LANGUASCO, PERELLI, ALBERTO
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The number of Goldbach representations of an integer [PDF]
, 2010 We prove the following result: Let $N \geq 2$ and assume the Riemann Hypothesis (RH) holds. Then \[ \sum_{n=1}^{N} R(n) =\frac{N^{2}}{2} -2 \sum_{\rho} \frac{N^{\rho + 1}}{\rho (\rho + 1)} + O(N \log^{3}N), \] where $\rho=1/2+i\gamma$ runs over the non ...
Languasco, Alessandro +1 more
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Exponentially small expansions of the Wright function on the Stokes lines [PDF]
, 2014 We investigate a particular aspect of the asymptotic expansion of the Wright function pΨq(z) for large |z|. In the case p = 1, q ⩾ 0, we establish the form of the exponentially small expansion of this function on certain rays in the z-plane (known as ...
Paris, Richard B.
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On the Ces\`aro average of the "Linnik numbers" [PDF]
, 2017 Let $\Lambda$ be the von Mangoldt function and $r_{Q}\left(n\right)=\sum_{m_{1}+m_{2}^{2}+m_{3}^{2}=n}\Lambda\left(m_{1}\right)$ be the counting function for the numbers that can be written as sum of a prime and two squares (that we will call Linnik ...
Cantarini, Marco
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