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Gauss Sum calculation

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#characters #exponential-sum #gauss-sums
33
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Gauss sum variant: $ \sum_{ a, b \in \mathbb{Z} } e^{-i \pi (a^2+b^2)/p } \big( e^{\pi(a-b)} + e^{-\pi(a-b)} \big) $

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#number-theory #mathematical-physics #gauss-sums
154
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Upper bound on the summation of roots of unity

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#number-theory #inequality #roots-of-unity #gauss-sums
175
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Proof of twisted Poisson summation formula using 'smoothed' Dirichlet characters?

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#number-theory #reference-request #gauss-sums #poisson-summation-formula #dirichlet-character
32
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Gauss sum involved in the Hecke action on classical Hilbert modular forms

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#modular-forms #gauss-sums #hecke-algebras #totally-real-field
103
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A problem with showing that $g_a^2=(-1)^{\tfrac{p-1}{2}}p$ for quadratic Gauss sums $g_a$

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#number-theory #prime-numbers #algebraic-number-theory #quadratic-residues #gauss-sums
34
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How does Ireland-Rosen reduce the coefficient of $z^{\frac{p-1}{2}}$ into this neat form in Kronecker proof of Gaussian sums?

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#number-theory #power-series #binomial-coefficients #exponentiation #gauss-sums
91
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A Relation between Dirichlet L functions for Quadratic Character and Gauss sums

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#number-theory #analytic-number-theory #characters #gauss-sums
32
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Question about Gauss Sums

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#number-theory #gauss-sums
63
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Help with summing characters

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#number-theory #summation #quadratic-residues #gauss-sums #jacobi-sums
185
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Question on a Gaussian sum and Jacobi sum identity

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#number-theory #solution-verification #gauss-sums #dirichlet-character #jacobi-sums
110
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$\chi(n)=\frac{\tau_k(\chi)}{\sqrt k}\sum_{m=1}^k \bar\chi(m)e^{-\frac{2\pi imn}{k}}$

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#number-theory #analytic-number-theory #characters #gauss-sums #dirichlet-character
437
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Writing a Gauss sum as a sum over divisors

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#number-theory #elementary-number-theory #algebraic-number-theory #analytic-number-theory #gauss-sums
53
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Summation Sequence

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#discrete-mathematics #summation #gauss-sums
145
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Summation Sequence Question

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#discrete-mathematics #summation #gauss-sums

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