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Results tagged with nt.number-theory
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user 106628
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
3
votes
1
answer
246
views
Non-lacunarity of Fourier coefficients
Let $f=\sum_{n\geq 1}a_n q^n$ be a non-CM newform of weight $\geq 2$. It is a classical result of Serre that if $A=\{p-\text{prime}~|~a_p=0\}$ then for $x\geq 2$: $$|A\cap [1,x]|\ll \frac{x}{(\log x)^ …
- 167
5
votes
1
answer
331
views
L-series of difference of two cusp forms
Let $f=\sum_{n\geq 1} a_nq^n$ and $g=\sum_{n\geq 1} b_nq^n$ be two distinct cusp eigenforms of same weight $k\geq 2$ with real Fourier coefficients. We normalize the coefficients by defining: $\wideti …
- 167