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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
140
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What is the value of $L'(1,\chi)$ where $\chi$ is the non-principal Dirichlet character modulo 4?

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#number-theory #analytic-number-theory #dirichlet-series #dirichlet-character
74
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The Dirichlet character modulo a prime number

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#elementary-number-theory #dirichlet-character
74
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$q$-expansion of Eisenstein series twisted by a Dirichlet character

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#complex-analysis #number-theory #fourier-series #modular-forms #dirichlet-character
20
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Dirichlet L-Funktion for non-principal charakters at s=1

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#complex-analysis #residue-calculus #dirichlet-character
56
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Dirichlet Green's function outside the sphere

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#greens-function #dirichlet-character #mirror-symmetry
847
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What's the idea of Dirichlet’s Theorem on Arithmetic Progressions proof?

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#number-theory #prime-numbers #arithmetic-progressions #l-functions #dirichlet-character
42
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The p-adic value of Dirichlet L-function at 1

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#p-adic-number-theory #l-functions #dirichlet-character
178
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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
68
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Converting polylogarithms to Dirichlet L functions

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#zeta-functions #polylogarithm #l-functions #dirichlet-character
76
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Two questions about Dirichlet's characters and roots of unity.

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#number-theory #analytic-number-theory #roots-of-unity #dirichlet-character
24
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If two characters agree on almost all primes then are they induced by same primitive characters?

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#number-theory #examples-counterexamples #analytic-number-theory #dirichlet-character
50
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Proving Dirichlet character is primitive

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#algebraic-number-theory #class-field-theory #dirichlet-character
102
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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
127
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Show that $\sum_{n\leq x}\frac{f(n)}{\sqrt n}=2L(1,\chi)\sqrt{x}+O(1)$, where $f(n)=\sum_{d\vert n}\chi(n)$.

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#number-theory #analytic-number-theory #l-functions #dirichlet-character

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