Results 21 to 30 of about 24,999 (231)
Fractional parts of polynomials over the primes [PDF]
, 2017 Let f be a polynomial with irrational leading coefficient. We obtain inequalities for the distance from the nearest integer of f(p) that hold for infinitely many primes p.
Baker, Roger
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On exponential sums over prime numbers [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1989 AbstractIn this article we establish an estimate for a sum over primes that is the analogue of an estimate for a sum over consecutive integers which has proved to be very useful in applications of exponential sums to problems in number theory.
Sárközy, A., Stewart, C. L.
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Exterior powers in Iwasawa theory
, 2021 The Iwasawa theory of CM fields has traditionally concerned Iwasawa modules that are abelian pro-p Galois groups with ramification allowed at a maximal set of primes over p such that the module is torsion.
Bleher, F. +5 more
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Real exponential sums over primes and prime gaps
, 2023 We prove that given $λ\in \R$ such that $0 < λ< 1$, then $π(x + x^λ) - π(x) \sim \displaystyle \frac{x^λ}{\log(x)}$. This solves a long-standing problem concerning the existence of primes in short intervals. In particular, we give a positive answer (for all sufficiently large number) to some old conjectures about prime numbers, such as Legendre's
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On Erdős sums of almost primes
Comptes Rendus. MathématiqueIn 1935, Erdős proved that the sums $f_k=\sum _n 1/(n\log n)$, over integers $n$ with exactly $k$ prime factors, are bounded by an absolute constant, and in 1993 Zhang proved that $f_k$ is maximized by the prime sum $f_1=\sum _p 1/(p\log p)$.
Gorodetsky, Ofir +2 more
doaj +1 more source
Riemann Hypothesis and Random Walks: the Zeta case
, 2017 In previous work it was shown that if certain series based on sums over primes of non-principal Dirichlet characters have a conjectured random walk behavior, then the Euler product formula for its $L$-function is valid to the right of the critical line $\
LeClair, André
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Three topics in additive prime number theory
, 2007 This is an expository article to accompany my two lectures at the CDM conference. I have used this an excuse to make public two sets of notes I had lying around, and also to put together a short reader's guide to some recent joint work with T.Tao ...
Green, Ben
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Objective To evaluate selumetinib exposure using therapeutic drug monitoring (TDM) in pediatric patients with neurofibromatosis type 1 (NF1) and plexiform neurofibromas (PN), assess interpatient pharmacokinetic variability, and explore the relationship between drug exposure, clinical response, and adverse effects.
Janka Kovács +8 more
wiley +1 more source
On certain exponential sums over primes
Journal of Number Theory, 2009 Let \(f(x)\) be a real valued polynomial of degree \(k\geq 4\) and irrational leading coefficient \(\alpha\). Exponential sums of the form \[ S:=\sum_{p\leq N} (\log p) e(f(p)) \] have received a lot of interest. \textit{G. Harman} proved in [Mathematika 28, 249--254 (1981; Zbl 0465.10029)] that if \(q\) is the denominator of a convergent of \(\alpha\),
Maier, H., Sankaranarayanan, A.
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Purpose Pediatric central nervous system (CNS) tumors often recur despite multimodality therapy. Although re‐irradiation (re‐RT) has historically been limited by concerns for severe late toxicities, modern techniques have renewed interest in this approach. Proton therapy provides dosimetric advantages that may enable curative re‐treatment with
Jin‐Ho Song +15 more
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