scholarly journals Ramanujan’s Elementary Method in Partition Congruences

2011 ◽  
pp. 13-21 ◽  
Author(s):  
Bruce C. Berndt ◽  
Chadwick Gugg ◽  
Sun Kim
Keyword(s):  
Partition Congruences ◽  
Elementary Method

Construction of systems of polynomial equations with exact p-Divisibility via the covering method

2014 ◽  
Vol 13 (06) ◽  
pp. 1450013 ◽  
Author(s):  
Francis N. Castro ◽  
Ivelisse M. Rubio
Keyword(s):  
Exponential Sums ◽  
Polynomial Equations ◽  
Prime Field ◽  
Elementary Method ◽  
Covering Method ◽  
Systems Of Polynomial Equations

We present an elementary method to compute the exact p-divisibility of exponential sums of systems of polynomial equations over the prime field. Our results extend results by Carlitz and provide concrete and simple conditions to construct families of polynomial equations that are solvable over the prime field.

An Elementary Method Guide for Limnology

Ecology ◽  
1975 ◽  
Vol 56 (5) ◽  
pp. 1231-1231
Author(s):  
Charles C. Davis
Keyword(s):  
Elementary Method

scholarly journals Gröbner bases and products of coefficient rings

2002 ◽  
Vol 65 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Graham H. Norton ◽  
Ana Sӑlӑgean
Keyword(s):  
Gröbner Basis ◽  
Chinese Remainder Theorem ◽  
Gröbner Bases ◽  
Commutative Rings ◽  
Grobner Bases ◽  
Grobner Basis ◽  
Know How ◽  
Elementary Method ◽  
Coefficient Ring ◽  
Finite Direct Product

Suppose that A is a finite direct product of commutative rings. We show from first principles that a Gröbner basis for an ideal of A[x1,…,xn] can be easily obtained by ‘joining’ Gröbner bases of the projected ideals with coefficients in the factors of A (which can themselves be obtained in parallel). Similarly for strong Gröbner bases. This gives an elementary method of constructing a (strong) Gröbner basis when the Chinese Remainder Theorem applies to the coefficient ring and we know how to compute (strong) Gröbner bases in each factor.

Hardy–Orlicz Spaces of Dirichlet Series: An Interpolation Problem on Abscissae of Convergence

2019 ◽  
Author(s):  
Maxime Bailleul ◽  
Pascal Lefèvre ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Dirichlet Series ◽  
Hardy Spaces ◽  
Upper Bound ◽  
Interpolation Problem ◽  
Orlicz Spaces ◽  
Elementary Method ◽  
Abscissa Of Convergence ◽  
Upper Bound Estimate

Abstract The study of Hardy spaces of Dirichlet series denoted by $\mathscr{H}^p$ ($p\geq 1$) was initiated in [7] when $p=2$ and $p=\infty $, and in [2] for the general case. In this paper we introduce the Orlicz version of spaces of Dirichlet series $\mathscr{H}^\psi $. We focus on the case $\psi =\psi _q(t)=\exp (t^q)-1,$ and we compute the abscissa of convergence for these spaces. It turns out that its value is $\min \{1/q\,,1/2\}$ filling the gap between the case $\mathscr{H}^\infty $, where the abscissa is equal to $0$, and the case $\mathscr{H}^p$ for $p$ finite, where the abscissa is equal to $1/2$. The upper-bound estimate relies on an elementary method that applies to many spaces of Dirichlet series. This answers a question raised by Hedenmalm in [6].

The Dirichlet Divisor Problem of Arithmetic Progressions

2016 ◽  
Vol 59 (3) ◽  
pp. 592-598
Author(s):  
H. Q. Liu
Keyword(s):  
Asymptotic Formula ◽  
Divisor Problem ◽  
Arithmetic Progressions ◽  
Elementary Method ◽  
Dirichlet Divisor Problem ◽  
Better Than

AbstractWe present an elementary method for studying the problem of getting an asymptotic formula that is better than Hooley’s and Heath-Brown’s results for certain cases.

Note on the probability distribution arising in the study of the Institute's examinations

1947 ◽  
Vol 6 (03) ◽  
pp. 140-143
Author(s):  
John Wishart
Keyword(s):  
Probability Distribution ◽  
Characteristic Function ◽  
Good Deal ◽  
Negative Index ◽  
Elementary Method ◽  
Mean And Variance ◽  
Full Power ◽  
The One

The distribution discussed by Mayhew and Vajda (J.S.S.Vol. vi, 1946, pp. 67–75 (70)), is the binomial with negative index (having origin, i.e. first term, atninstead ofo), about which a good deal has been written, and their problem is the one discussed by Yule in 1910 (J.R. Statist. Soc.Vol. LXXIII, p. 26). The authors base their proof on an idea of Laplace, but the full power of the characteristic function derivation can be seen if we go further than they did. The results are of some interest, particularly as Kendall (Advanćed Theory of Statistics, Vol. 1, §5.13) does not go beyond deriving mean and variance by the elementary method in this case.

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