Gauss Sums, Quadratic Reciprocity, and the Jacobi Symbol

2018 ◽  
pp. 119-130
Author(s):  
Ramin Takloo-Bighash
Keyword(s):  
Gauss Sums ◽  
Quadratic Reciprocity ◽  
Jacobi Symbol

scholarly journals Postcards from the Edge, or Snapshots of the Theory of Generalised Moonshine

2002 ◽  
Vol 45 (4) ◽  
pp. 606-622
Author(s):  
Terry Gannon
Keyword(s):  
Number Theory ◽  
Gauss Sums ◽  
Quadratic Reciprocity ◽  
The Impact

AbstractWe begin by reviewing Monstrous Moonshine. The impact of Moonshine on algebra has been profound, but so far it has had little to teach number theory. We introduce (using ‘postcards’) a much larger context in which Monstrous Moonshine naturally sits. This context suggests Moonshine should indeed have consequences for number theory. We provide some humble examples of this: new generalisations of Gauss sums and quadratic reciprocity.

scholarly journals The Mean Values of Character Sums and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 318
Author(s):  
Jiafan Zhang ◽  
Yuanyuan Meng
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Mean Values ◽  
Special Polynomials ◽  
Elementary Methods ◽  
The Mean

In this paper, we use the elementary methods and properties of classical Gauss sums to study the calculation problems of some mean values of character sums of special polynomials, and obtained several interesting calculation formulae for them. As an application, we give a criterion for determining that 2 is the cubic residue for any odd prime p.

scholarly journals A note on two-term exponential sum and the reciprocal of the quartic Gauss sums

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wenpeng Zhang ◽  
Xingxing Lv
Keyword(s):  
Exponential Sums ◽  
Exponential Sum ◽  
Gauss Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

AbstractThe main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.

scholarly journals Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets

1999 ◽  
Vol 87 (1) ◽  
pp. 74-119 ◽  
Author(s):  
Ronald Evans ◽  
Henk D.L. Hollmann ◽  
Christian Krattenthaler ◽  
Qing Xiang
Keyword(s):  
Difference Sets ◽  
Gauss Sums ◽  
Cyclic Difference Sets ◽  
Jacobi Sums

scholarly journals Elliptic Gauss sums and applications to point counting

2010 ◽  
Vol 45 (8) ◽  
pp. 825-836 ◽  
Author(s):  
Preda Mihăilescu ◽  
Victor Vuletescu
Keyword(s):  
Gauss Sums ◽  
Point Counting

scholarly journals On the quartic Gauss sums and their recurrence property

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Shimeng Shen ◽  
Wenpeng Zhang
Keyword(s):  
Gauss Sums ◽  
Recurrence Property

scholarly journals On the law of quadratic reciprocity

1935 ◽  
Vol 41 (6) ◽  
pp. 359-361 ◽  
Author(s):  
Albert Whiteman
Keyword(s):  
Quadratic Reciprocity ◽  
The Law

Quadratic Gauss Sums

1982 ◽  
pp. 66-78
Author(s):  
Kenneth Ireland ◽  
Michael Rosen
Keyword(s):  
Gauss Sums
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