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The first moment of primes in arithmetic progressions: beyond the Siegel–Walfisz range
Transactions of the London Mathematical Society, 2021 We investigate the first moment of primes in progressions ∑q⩽x/N(q,a)=1ψ(x;q,a)−xφ(q)as x,N→∞. We show unconditionally that, when a=1, there is a significant bias towards negative values, uniformly for N⩽eclogx.
Sary Drappeau, Daniel Fiorilli
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Bakewell Primary School newsletter
, 2020 Fortnightly during school terms.An Independent Public School Delivering Excellence in EducationMade available via the Publications (Legal Deposit) Act 2004 (NT).This publication contains many links to external sites. These external sites may no longer be
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Bakewell Primary School newsletter
, 2019 Fortnightly during school terms.An Independent Public School Delivering Excellence in EducationMade available via the Publications (Legal Deposit) Act 2004 (NT).This publication contains many links to external sites. These external sites may no longer be
core +15 more sources
Bakewell Primary School newsletter
, 2018 Fortnightly during school terms.An Independent Public School Delivering Excellence in EducationMade available via the Publications (Legal Deposit) Act 2004 (NT).This publication contains many links to external sites. These external sites may no longer be
core +11 more sources
Large oscillations of the argument of the Riemann zeta‐function
Bulletin of the London Mathematical Society, Volume 53, Issue 6, Page 1776-1785, December 2021., 2021 Abstract Let S(t) denote the argument of the Riemann zeta‐function, defined as S(t)=1πImlogζ(1/2+it).Assuming the Riemann hypothesis, we prove that S(t)=Ω±logtlogloglogtloglogt.This improves the classical Ω‐results of Montgomery (Theorem 2; Comment. Math. Helv. 52 (1977) 511–518) and matches with the Ω‐result obtained by Bondarenko and Seip (Theorem 2;
Andrés Chirre, Kamalakshya Mahatab
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Linear correlations of multiplicative functions
Proceedings of the London Mathematical Society, Volume 121, Issue 2, Page 372-425, August 2020., 2020 Abstract We prove a Green–Tao type theorem for multiplicative functions.
Lilian Matthiesen
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SECOND MOMENTS IN THE GENERALIZED GAUSS CIRCLE PROBLEM
Forum of Mathematics, Sigma, 2018 The generalized Gauss circle problem concerns the lattice point discrepancy of large spheres. We study the Dirichlet series associated to $P_{k}(n)^{2}$, where $P_{k}(n)$ is the discrepancy between the volume of the $k$-dimensional sphere of radius ...
THOMAS A. HULSE +3 more
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VALUE PATTERNS OF MULTIPLICATIVE FUNCTIONS AND RELATED SEQUENCES
Forum of Mathematics, Sigma, 2019 We study the existence of various sign and value patterns in sequences defined by multiplicative functions or related objects. For any set $A$ whose indicator function is ‘approximately multiplicative’ and uniformly distributed on short intervals in a ...
TERENCE TAO, JONI TERÄVÄINEN
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Systems for the management of respiratory disease in primary care - an international series: United Kingdom [PDF]
, 2010 INTRODUCTION: The UK National Health Service (NHS) is essentially publicly funded through general taxation. Challenges facing the NHS include the rise in prevalence of long-term conditions and financial pressures.
Allison Worth +14 more
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ON BINARY CORRELATIONS OF MULTIPLICATIVE FUNCTIONS
Forum of Mathematics, Sigma, 2018 We study logarithmically averaged binary correlations of bounded multiplicative functions $g_{1}$ and $g_{2}$ . A breakthrough on these correlations was made by Tao, who showed that the
JONI TERÄVÄINEN
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