On the Distribution of αp Modulo One in Quadratic Number Fields
References
- BAIER, S.—TECHNAU, M.: On the distribution ofαp modulo one in imaginary quadratic number fields with class number one, J. Théor. Nombres Bordeaux. 32 (2020), no. 3, 719–760.<a href="https://doi.org/10.5802/jtnb.1141" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.5802/jtnb.1141</a>
- BAIER, S.—MAZUMDER, D.: Diophantine approximation with prime restriction in real quadratic number fields, Math. Z. 2021.http://link.springer.com/article/<a href="https://doi.org/10.1007/s00209-021-02705-x10.1007/s00209-021-02705-x" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/s00209-021-02705-x10.1007/s00209-021-02705-x</a>
- COLEMAN, M. D.: . The Rosser-Iwaniec sieve in number fields, with an application, Acta Arith. 65 (1993), no. 1, 53–83.<a href="https://doi.org/10.4064/aa-65-1-53-83" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.4064/aa-65-1-53-83</a>
- FOGELS, E.: On the zeros of Hecke’s L-functions. I, II, Acta Arith. 7 (1962) 87–106, 131–147.<a href="https://doi.org/10.4064/aa-7-2-131-147" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.4064/aa-7-2-131-147</a>
- HARMAN, G.: On the distribution of αp modulo one. J. London Math. Soc. 27 (1983), no. 2, 9–18.<a href="https://doi.org/10.1112/jlms/s2-27.1.9" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1112/jlms/s2-27.1.9</a>
- HARMAN, G.: On the distribution of αp modulo one. II, Proc. London Math. Soc. 72 (1996), no. 3, 241–260.<a href="https://doi.org/10.1112/plms/s3-72.2.241" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1112/plms/s3-72.2.241</a>
- HARMAN, G.: Prime-detecting Sieves.In: London Mathematical Society Monographs Series, Vol. 33. Princeton University Press, Princeton, N J, 2007.
- HARMAN, G.: Diophantine approximation with Gaussian primes, Q. J. Math. 70 (2019), no. 4, 1505–1519.<a href="https://doi.org/10.1093/qmathj/haz038" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1093/qmathj/haz038</a>
- HECKE, E.: Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen. I, Math. Z. 1 (1918), 357–376.<a href="https://doi.org/10.1007/BF01465095" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/BF01465095</a>
- HECKE, E.: Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen. II, Math. Z. 6 (1920), 11–51.<a href="https://doi.org/10.1007/BF01202991" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1007/BF01202991</a>
- IWANIEC, H.: Rosser’s Sieve, Acta Arith. 36 (1980), 171–202.<a href="https://doi.org/10.4064/aa-36-2-171-202" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.4064/aa-36-2-171-202</a>
- IWANIEC, H.—KOWALSKI, E.: Analytic Number Theory.In: American Mathematical Society Colloquium Publications, Vol. 53. American Mathematical Society (AMS), Providence, RI, 2004.<a href="https://doi.org/10.1090/coll/053" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1090/coll/053</a>
- JIA, C.: On the distribution of αp modulo one, J. Number Theory 45 (1993), 241–253.<a href="https://doi.org/10.1006/jnth.1993.1075" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1006/jnth.1993.1075</a>
- MATOMÄKI, K.: The distribution of αp modulo one, Math. Proc. Camb. Philos. Soc. 147 (2009), no. 2, 267–283.<a href="https://doi.org/10.1017/S030500410900245X" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1017/S030500410900245X</a>
- MONTGOMERY, H. L.—VAUGHAN, R. C.: Multiplicative Number Theory. I. Classical Theory.In: Cambridge Studies in Advanced Mathematics, Vol. 97. Cambridge University Press, Cambridge, 2007.<a href="https://doi.org/10.1017/CBO9780511618314" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1017/CBO9780511618314</a>
- TENENBAUM G.: Introduction to Analytic and Probabilistic Number Theory.(3rd expanded ed.) In: Graduate Studies in Mathematics, Vol. 163. American Mathematical Society (AMS), Providence, RI, 2015.<a href="https://doi.org/10.1090/gsm/163" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1090/gsm/163</a>
Language: English
Page range: 1 - 48
Submitted on: Apr 27, 2021
Accepted on: Aug 12, 2021
Published on: Feb 2, 2022
Published by: Slovak Academy of Sciences
In partnership with: Paradigm Publishing Services
Publication frequency: 2 times per year
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© 2022 Stephan Baier, Dwaipayan Mazumder, Marc Technau, published by Slovak Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.