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Starting from a classical generating series for Bessel functions due to Schl¨omilch[4], we use Dwork’s relative dual theory to broadly generalize unit-root results of Dwork[3] on Kloosterman sums and ...
(k+1)-sums versus k-sums     (k+1)-sums  k-sums       2010/11/23
Given $k\in \mathbb{N}$ and a subset $A=\{a_{1},...,a_{n}\}$ of $n$ integers, we define $S_{k}=S_{k}(A)=\{\sum_{I}a_{i}:I\in [n]^{(k)}\}$, i.e. $S_{k}$ is the set of integers that may be expressed as...
We show that if the fundamental groups of the complements of two line arrangements in the complex projective plane are isomorphic to the same direct sum of free groups, then the complements of the arr...
We discuss, both for systems of complex vector fields and for sums of squares, the phenomenon discovered by Kohn of hypoellipticity with loss of derivatives.MSC: 32W05, 32W25, 32T25
Sums of five Almost Equal Prime Squares          2007/12/12
In this paper we sharpen Hua's result by proving that each sufficiently large integer $N$ congruent to 5 modulo 24 can be written as $$N=p_1^2+p_2^2+p_3^2+p_4^2+p_5^2, \mbox{ with } |p_j-\sqrt{N/5}| \...
Some maximal moment inequalities for partial sums of the strong mixing random variable sequence are established. These inequalities use moment sums as up-boundary and improve the corresponding ones ob...

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