Results 1 to 10 of about 273 (50)
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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On a basic mean value Theorem with explicit exponents [PDF]
, 2020 In this paper we follow a paper from A. Sedunova (2017) regarding R. C. Vaughan's basic mean value Theorem (Acta Arith. 1980) to improve and complete a more general demonstration for a suitable class of arithmetic functions as started by A. C.
Ferrari, Matteo
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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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Odd values of the Klein j-function and the cubic partition function [PDF]
, 2015 In this note, using entirely algebraic or elementary methods, we determine a new asymptotic lower bound for the number of odd values of one of the most important modular functions in number theory, the Klein $j$-function.
Zanello, Fabrizio
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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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Correction to ‘Shifted convolution and the Titchmarsh divisor problem over Fq[t] [PDF]
, 2016 PublishedCorrection to original article: Phil. Trans. R. Soc. A 373, 20140308 (28 April 2015; Published online 23 March 2015) (doi:10.1098/rsta.2014.0308). Two of the equations in the original article contained a typographical error.
Andrade, JC, Bary-Soroker, L, Rudnick, Z
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On the number of subgroups of a given exponent in a finite abelian group [PDF]
, 2017 This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups.
Tóth, László, Tărnăuceanu, Marius
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Variations on a theorem of Davenport concerning abundant numbers [PDF]
, 2013 Let \sigma(n) = \sum_{d \mid n}d be the usual sum-of-divisors function. In 1933, Davenport showed that that n/\sigma(n) possesses a continuous distribution function. In other words, the limit D(u):= \lim_{x\to\infty} \frac{1}{x}\sum_{n \leq x,~n/\sigma(n)
Jennings, Emily +2 more
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Exceptional sets in Waring's problem: two squares and s biquadrates [PDF]
, 2014 Let $R_s(n)$ denote the number of representations of the positive number $n$ as the sum of two squares and $s$ biquadrates. When $s=3$ or $4$, it is established that the anticipated asymptotic formula for $R_s(n)$ holds for all $n\le X$ with at most $O(X^
Zhao, Lilu
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