Abstract
We estimate the number of primes represented by a general quadratic polynomial with discriminant \(\Delta \), assuming that the corresponding real character is exceptional.
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References
Friedlander, J., Iwaniec, H.: Opera de Cribro. American Mathematical Society Colloquium Publications, vol. 57. American Mathematical Society, Providence, RI (2010)
Friedlander, J.B., Iwaniec, H.: Exceptional discriminants are the sum of a square and a prime. Q. J. Math. 64(4), 1099–1107 (2013)
Granville, A., Mollin, R.A.: Rabinowitsch revisited. Acta Arith. 96(2), 139–153 (2000)
Hardy, G.H., Littlewood, J.E.: Some problems of ‘Partitio numerorum’; III: on the expression of a number as a sum of primes. Acta Math. 44(1), 1–70 (1923)
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Fernando Chamizo is partially supported by the MTM2017-83496-P Grant of the MICINN (Spain) and by “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554). This latter grant supported the visit of Jorge Jiménez Urroz to the ICMAT where this work was completed. The second author is partially supported by the PID2019-110224RB-I00 Grant of the MICINN (Spain)
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Chamizo, F., Jiménez Urroz, J. Primes represented by quadratic polynomials via exceptional characters. Arch. Math. 117, 147–154 (2021). https://doi.org/10.1007/s00013-021-01602-3
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DOI: https://doi.org/10.1007/s00013-021-01602-3