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A Diophantine problem with prime variables
Diophantine problems with prime variables Number Theory
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2012/6/14
We study the distribution of the values of the form $\lambda_1 p_1 + \lambda_2 p_2 + \lambda_3 p_3^k$, where $\lambda_1$, $\lambda_2$ and $\lambda_3$ are non-zero real number not all of the same sign,...
Ramanujan type congruences for modular forms of several variables
Congruences for modular forms Cusp forms Number Theory
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2012/4/17
We give congruences between the Eisenstein series and a cusp form in the cases of Siegel modular forms and Hermitian modular forms. We should emphasize that there is a relation between the existence o...
Precise rates in the law of iterated logarithm for the moment of I.I.D. random variables
the law of iterated logarithm strong approximation truncation method i.i.d. random variables
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2007/12/12
Let $\{X, X_n; n\ge 1\}$ be a sequence of i.i.d. random variables, ${\rm E} X=0$, ${\rm E} X^2=\sigma^2<\infty$. Set $S_n=X_1+X_2+\cdots+X_n$, $M_n=\max_{k\le n}|S_k|$, $n\ge 1$. Let $a_n=O(1/\log\log...