Chen's double sieve, Goldbach's conjecture and the twin prime problem
We give a more comrehensive treatment of Chen's double sieve and improve related constants in Goldbach's conjecture and the twin prime problem.
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arXiv subjects
Jie Wu
Publications and source records attributed to Jie Wu.
Special values of symmetric power $L$-functions and Hecke eigenvalues
We compute the moments of L-functions of symmetric powers of modular forms at the edge of the critical strip, twisted by the central value of the L-functions of modular forms. We show that, in the case of even powers, it is equivalent to twist by the value at the edge of the critical strip of the symmetric square L-functions. We deduce information on the size of symmetric power L-functions at the edge of the critical strip under conditions. In a second part, we study the distribution of small and large Hecke eigenvalues. We deduce information on the simultaneous extremality conditions on the values of L-functions of symmetric powers of modular forms at the edge of the critical strip.
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The universality of symmetric power L-functions and their Rankin-Selberg L-functions
We establish the universality theorem for the first four symmetric power L-functions of automorphic forms and their associated Rankin-Selberg L-functions. This generalizes some results of Laurincikas & Matsumoto and Matsumoto respectively.
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Small gaps in coefficients of L-functions and B-free numbers in small intervals
We discuss questions related to the non-existence of gaps in the series defining modular forms and other arithmetic functions of various types, and improve results of Serre, Balog and Ono, and Alkan, using new results about exponential sums and the distribution of $B$-free numbers.
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A braided simplicial group
By studying braid group actions on Milnor's construction of the 1-sphere, we show that the general higher homotopy group of the 3-sphere is the fixed set of the pure braid group action on certain combinatorially described group. We also give certain representation of higher differentials in the Adams spectral sequence for the homotopy groups of the 2-sphere.
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A Product Decomposition of $Ω^3_0Σ${\bf R}$P^2$
We give a specific product decomposition of the base-point path connected component of the triple loop space of the suspension of the projective plane.
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On Combinatorial Calculations for the James--Hopf maps
We give some formulas of the James-Hopf maps by using combinatorial methods. An application is to give a product decomposition of the spaces $ΩΣ^2(X)$.
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On the Homology of Configuration Spaces $C((M,M_o)\times {\bold R}^n; X)$
The homology with coefficients in a field of the configuration spaces $C(M\times \bold R ^n,M_o\times \bold R ^n;X)$ is determined in this paper.
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On Combinatorial Descriptions of Homotopy Groups of $ΣK(π,1)$
We give a combinatorial description of homotopy groups of $ΣK(π,1)$. In particular, all of the homotopy groups of the $3$-sphere are combinatorially given.
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