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Beyond Beatty sequences: Complementary lattices
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- Journal:
- Canadian Mathematical Bulletin / Volume 64 / Issue 3 / September 2021
- Published online by Cambridge University Press:
- 06 August 2020, pp. 499-511
- Print publication:
- September 2021
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Irregularities in the Distribution of Prime Numbers in a Beatty Sequence
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 63 / Issue 4 / December 2020
- Published online by Cambridge University Press:
- 16 December 2019, pp. 738-743
- Print publication:
- December 2020
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We prove irregularities in the distribution of prime numbers in any Beatty sequence
${\mathcal{B}}(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD})$, where 
$\unicode[STIX]{x1D6FC}$ is a positive real irrational number of finite type.
Cancellation of Cusp Forms Coefficients over Beatty Sequences on GL(m)
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- Journal:
- Canadian Mathematical Bulletin / Volume 54 / Issue 4 / 01 December 2011
- Published online by Cambridge University Press:
- 20 November 2018, pp. 757-762
- Print publication:
- 01 December 2011
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Let
$A({{n}_{1}},\,{{n}_{2}},\ldots ,\,{{n}_{m}}-1)$ be the normalized Fourier coefficients of a Maass cusp form on 
$\text{GM(}m\text{)}$ . In this paper, we study the cancellation of $A({{n}_{1}},\,{{n}_{2}},\ldots ,\,{{n}_{m}}-1)$ over Beatty sequences.
