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Can a bound be given to $\sum_{a=1}^{p-1}\chi(a)\left(\frac{a^2-1}{p}\right)$, which is smaller than $p$, where $\chi$ is a dirichlet character?

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#number-theory #algebraic-number-theory #upper-lower-bounds #gauss-sums
121
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Sub-Sum of Roots of Unity

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#galois-theory #roots-of-unity #cyclotomic-fields #gauss-sums #algebraic-numbers
192
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Quadratic Gauss Sum with Jacobi Symbol of even nonsquare free Modulus

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#number-theory #arithmetic-functions #gauss-sums #jacobi-symbol
1k
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Trig identities analogous to $\tan(\pi/5)+4\sin(\pi/5)=\sqrt{5+2\sqrt{5}}$

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#trigonometry #prime-numbers #modular-arithmetic #gauss-sums #algebraic-numbers
160
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Imprimitive Dirichlet characters as sum of additive characters

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#number-theory #analytic-number-theory #characters #gauss-sums
7.7k
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Sum of even numbers N?

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#summation #arithmetic-progressions #gauss-sums
42
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The sum $\sum_{t \not \mod - 1} \chi[t(t + 1)]$

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#number-theory #gauss-sums
82
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Finding a formula for $(1^3)\cdot(n)+(2^3)\cdot(n-1)+(3^3)\cdot(n-2)+ \cdots + (n^3)\cdot(1)$

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#summation #gauss-sums
700
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Equivalent definitions of the quadratic gauss sum

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#elementary-number-theory #gauss-sums
451
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Properties of a Jacobi sum for $p=1\bmod 4$

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#elementary-number-theory #gauss-sums
68
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Help Engineering maths

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#ordinary-differential-equations #gauss-sums
594
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Decompose a sum of Gaussian curves

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#statistics #statistical-inference #gauss-sums
456
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Gamma function and Gauss sums

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#number-theory #gamma-function #gauss-sums
327
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Absolute value of a cubic Gauss sum (over Field $\mathbb{F}_p$ )

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#number-theory #reference-request #finite-fields #exponential-sum #gauss-sums
355
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Dirichlet character modulo p

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#complex-analysis #number-theory #analytic-number-theory #characters #gauss-sums

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