Riv. Mat. Univ. Parma, Vol. 12, No. 1, 2021

John Friedlander [a] and Henryk Iwaniec [b]

Sums over vanishing determinants

Pages: 49-62
Received: 3 February 2020
Accepted in revised form: 19 March 2020
Mathematics Subject Classification (2010): 11N25, 11N56.
Keywords: Gaussian integers, large sieve inequality.
Authors address:
[a]: University of Toronto, 1265 Military Trail, Toronto, ON M1C 1A4, Canada
[b]: Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08903, USA

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Abstract: In analytic number theory one frequently needs to estimate various bilinear sums, in particular exponentials with Kloosterman type fractions. Here, we establish bounds which go beyond the straight-forward approach.

J. B. Friedlander and H. Iwaniec, The polynomial \(X^2+Y^4\) captures its primes, Ann. of Math. 148 (1998), 945-1040. MR1670065
J. B. Friedlander and H. Iwaniec, Coordinate distribution of Gaussian primes, J. Eur. Math. Soc. (JEMS), online first, DOI: 10.4171/JEMS/1083.

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