Valentin Blomer
Past graduate courses:
- Theory of character sums (Problem set: Set 1, Set 2, Set 3, Set 3, Set 5)
- Spectral methods of automorphic forms (Problem sets: Set 1, Set 2, Set 3, Set 4, Set 5)
- Algebra (Problem sets: Set 1, Set 2, Set 3, Set 4, Set 5, Set 6, Set 7, Set 8, Set 9, Set 10, Set 11, Set 12, Set 13, Set 14, Set 15, Set 16, Set 17, Set 18, Set 19)
- Introduction to Modular Forms
- Introduction to Analytic Number Theory (in Göttingen)
- Elliptic Curves and Cryptography (in Göttingen)
Mathematics Research
My area of research is analytic number
theory, in particular
- automorphic forms and L-functions, and
- quadratic forms and their arithmetic applications.
Here's a list of my recent journal articles
- Thin bases of order h, Journal of Number Theory 98 (2003),
34-46 (abstract)
- On cusp forms associated with binary theta series, Archiv der Mathematik 82 (2004), 140-146 (abstract)
- Binary quadratic forms with large discriminants and sums of
two squareful integers,
Crelle's Journal 569 (2004), 213-234 (abstract)
- Uniform bounds for Fourier coefficients of theta series with
arithmetic applications, Acta Arithmetica 114, (2004), 1-21 (abstract)
- Shifted convolution sums and subconvexity bounds for automorphic L-functions, IMRN 2004, no. 73, 3905-3926 (abstract)
- Nonvanishing of class group L-functions at the central point, Annales de l'Institut Fourier 54 (2004), 831-847 (abstract)
- Binary quadratic forms with large discriminants and sums of
two squareful integers
II, J. London Math. Soc. 71 (2005), 69-84 (abstract)
- A three squares theorem with almost primes (with J. Brüdern),
Bulletin of the London Mathematical Society 37 (2005), 507-513 (abstract)
- Rankin-Selberg L-functions on the critical line, manuscripta mathematica 117 (2005), 111-133 (abstract)
- Uniform bounds for the number of integers represented by systems
of Abelian norm forms (with J.-C. Schlage-Puchta), Acta Arith. 123 (2006), 183-199 (abstract)
- Estimates for representation numbers of quadratic forms (with A. Granville), Duke Math. Journal 135 (2006), 261-302 (abstract)
- A Burgess-like subconvex bound for twisted L-functions (with appendix 2 by Z.Mao) (with G. Harcos and P. Michel), Forum Math. 19 (2007), 61-106 (abstract)
- Bounds for modular L-functions in the level aspect (with G.Harcos and P.Michel), Ann. Sci. Ecole Norm. Sup. 40 (2007), 697-740 (abstract)
- Prime paucity for sums of two squares (with J. Brüdern), Bull. Lond. Math. Soc. 40 (2008), 457-462 (abstract)
- Sums of Hecke eigenvalues over values of quadratic polynomials, IMRN 2008 art. ID rnn059, 29pp. (abstract, arxiv)
- Hybrid bounds for twisted L-functions (with G. Harcos), Crelle's Journal 621 (2008), 53-79 (abstract)
- Ternary quadratic forms, and sums of three squares with restricted variables, in: The anatomy of integers, CRM proceedings & lecture notes 46 (2008), 1-17 (abstract)
- Spectral decomposition of shifted convolution sums (with G. Harcos), Duke Math. J. 144 (2008), 321-339 (abstract, arxiv)
- The average value of divisor sums in arithmetic progressions, Quart. J. Math. 59 (2008), 275-286 (abstract)
- On the central value of symmetric square L-functions, Math. Z. 260 (2008), 755-777 (abstract)
- A quadric with arithmetic paucity (with J. Brüdern), 10pp., to appear in Quart. J. Math. (abstract)
- The number of integer points on Vinogradov's quadric (with J. Brüdern), 10pp., to appear in Monatsh. Math. (abstract)
- Iterates of Vinogradov's quadric and prime paucity (with J. Brüdern), 10pp., to appear in Michigan Math. J.
- Sums of smooth squares (with
J. Brüdern and R. Dietmann), 40pp., to appear in Compositio Math. (abstract)
and preprints (submitted)
- Bounding sup-norms of cusp forms of large level (with R. Holowinsky), 20pp. (abstract, arxiv)
- Friable values of binary forms (with A. Balog, C. Dartyge, G. Tenenbaum), 20pp. (abstract)
- Twisted L-functions over number fields and Hilbert's eleventh problem (with G. Harcos), 45pp. (arxiv)
I provide copies of these papers on request. The arxiv versions may differ from the published versions.
Some pictures
Johanna
Oberwolfach, 2003
Banff, 2004
Oberwolfach, 2008
A Night in Tunesia
Last Update:
Jan 2009
