Results 11 to 20 of about 845 (61)
Journal of the London Mathematical Society, Volume 103, Issue 4, Page 1618-1642, June 2021., 2021 Abstract We consider partial sums of a weighted Steinhaus random multiplicative function and view this as a model for the Riemann zeta function. We give a description of the tails and high moments of this object. Using these we determine the likely maximum of TlogT independently sampled copies of our sum and find that this is in agreement with a ...
Marco Aymone, Winston Heap, Jing Zhao
wiley +1 more source
Estimates of convolutions of certain number‐theoretic error terms
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 1, Page 1-23, 2004., 2004 Several estimates for the convolution function C [f(x)]:=∫1xf(y) f(x/y)(dy/y) and its iterates are obtained when f(x) is a suitable number‐theoretic error term. We deal with the case of the asymptotic formula for ∫0T|ζ(1/2+it)|2kdt(k = 1, 2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the ...
Aleksandar Ivić
wiley +1 more source
Consecutive evaluation of Euler sums
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 9, Page 555-561, 2002., 2002 We describe a simple method for a consecutive evaluation of the Euler sums S(r, p), r = 1, 2, … in terms of zeta values.
Khristo N. Boyadzhiev
wiley +1 more source
A quantum field theoretical representation of Euler‐Zagier sums
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 3, Page 127-148, 2002., 2002 We establish a novel representation of arbitrary Euler‐Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve Bernoulli polynomials and Clausen functions to arbitrary orders.
Uwe Müller, Christian Schubert
wiley +1 more source
A note on the gaps between consecutive zeros of the Riemann zeta-function [PDF]
, 2009 Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and infinitely often they differ by at least 2.69 times the average spacing ...
Bui, H. M., Milinovich, M. B., Ng, N.
core +4 more sources
Simultaneous generation for zeta values by the Markov-WZ method [PDF]
, 2008 By application of the Markov-WZ method, we prove a more general form of a bivariate generating function identity containing, as particular cases, Koecher's and Almkvist-Granville's Ap\'ery-like formulae for odd zeta values. As a consequence, we get a new
Kh. Hessami +2 more
core +7 more sources
Evaluation of integrals with hypergeometric and logarithmic functions
Open Mathematics, 2018 We provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions.
Sofo Anthony
doaj +1 more source
A Note on Colored Tornheim's Double Series
, 2009 In this short note, we provide an explicit formula to compute every colored double Tornheim's series by using double polylogarithm values at roots of unity.
Zhao, Jianqiang
core +1 more source
Some hypergeometric integrals for linear forms in zeta values
, 2018 We prove integral representations of the approximation forms in zeta values constructed in arXiv:1801.09895 and arXiv:1803.08905.Comment: 3 ...
Zudilin, Wadim
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Analytic ranks of elliptic curves over number fields
, 2020 Let $E$ be an elliptic curves over the rational numbers. Let $F$ be a cyclic extension of prime degree $l$. Then, we show that the average of analytic ranks of $E(F)$ over all cyclic extension of prime degree $l$ is at most $2+r_\mathbb{Q}(E)$, where $r_\
Cho, Peter J.
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